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A sample is just a portion or subset of the entire population. So we know now the definition of population and sample. The other two types, parameter and statistics. 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This year we developed a new method for teaching and our goal is to see if the new method is better than method A which was used in last year. So we want to see if there is a big difference between scores or the average scores last year and this year. The same you can do for your weight. 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And our goal is to reduce their weights. Suppose they have a regime or diet for three months or exercise, whatever it is, then after three months, we have new weights for these persons. And we want to see if the diet is effective. 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Is it clear? So there are many, many reasons behind using statistics and collecting data. Now, what are the sources of data? Since statistics mainly, first step, we have to collect data. Now, what are the sources of the data? Generally speaking, there are two sources. 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What do you think is the difference between these two? I mean, what's the difference between primary and secondary sources? The primary source is the collector of the data. He is the analyzer. He analyzes it. 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So the primary sources means the researcher by himself. He should collect the data, then he can use the data to do his analysis. That's for the primary. Now, the primary could be data from political survey. 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We have two groups, maybe healthy people and patient people. So that's experimental group. Or observed data. That's the primary sources. Secondary sources, the person performing data analysis is not the data collector. 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But secondary, you can use the data that is published in the internet, for example, in the books, in governments and NGOs and so on. So these are the two sources of data. Sources of data fall into four categories. 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A design experiment is primary because you have to design the experiment, a survey. It's also primary. An observational study is also a primary source. So you have to distinguish between a primary and secondary sources. Any question? Comments? Next.", "tokens": [407, 300, 311, 11396, 4009, 13, 316, 1715, 5120, 307, 6194, 570, 291, 362, 281, 1715, 264, 5120, 11, 257, 8984, 13, 467, 311, 611, 6194, 13, 1107, 9951, 1478, 2979, 307, 611, 257, 6194, 4009, 13, 407, 291, 362, 281, 20206, 1296, 257, 6194, 293, 11396, 7139, 13, 2639, 1168, 30, 2432, 1117, 30, 3087, 13], "avg_logprob": -0.1807650849223137, "compression_ratio": 1.6646706586826348, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 540.17, "end": 540.55, "word": " So", "probability": 0.88330078125}, {"start": 540.55, "end": 541.19, "word": " that's", "probability": 0.9462890625}, {"start": 541.19, "end": 541.79, "word": " secondary", "probability": 0.92333984375}, {"start": 541.79, "end": 543.17, "word": " source.", "probability": 0.81640625}, {"start": 544.07, "end": 544.49, "word": " A", "probability": 0.8046875}, {"start": 544.49, "end": 544.89, "word": " design", "probability": 0.4140625}, {"start": 544.89, "end": 545.47, "word": " experiment", "probability": 0.60791015625}, {"start": 545.47, "end": 545.77, "word": " is", "probability": 0.53369140625}, {"start": 545.77, "end": 546.17, "word": " primary", "probability": 0.8134765625}, {"start": 546.17, "end": 546.95, "word": " because", "probability": 0.65087890625}, {"start": 546.95, "end": 547.23, "word": " you", "probability": 0.9638671875}, {"start": 547.23, "end": 547.83, "word": " have", "probability": 0.953125}, {"start": 547.83, "end": 548.11, "word": " to", "probability": 0.97314453125}, {"start": 548.11, "end": 549.09, "word": " design", "probability": 0.97802734375}, {"start": 549.09, "end": 549.61, "word": " the", "probability": 0.8974609375}, {"start": 549.61, "end": 550.11, "word": " experiment,", "probability": 0.9541015625}, {"start": 550.21, "end": 550.35, "word": " a", "probability": 0.9677734375}, {"start": 550.35, "end": 550.63, "word": " survey.", "probability": 0.89794921875}, {"start": 551.13, "end": 551.59, "word": " It's", "probability": 0.982666015625}, {"start": 551.59, "end": 551.85, "word": " also", "probability": 0.8818359375}, {"start": 551.85, "end": 552.25, "word": " primary.", "probability": 0.9248046875}, {"start": 552.81, "end": 552.95, "word": " An", "probability": 0.50146484375}, {"start": 552.95, "end": 554.23, "word": " observational", "probability": 0.8408203125}, {"start": 554.23, "end": 554.61, "word": " study", "probability": 0.93359375}, {"start": 554.61, "end": 554.79, "word": " is", "probability": 0.94775390625}, {"start": 554.79, "end": 555.23, "word": " also", "probability": 0.87890625}, {"start": 555.23, "end": 556.29, "word": " a", "probability": 0.99072265625}, {"start": 556.29, "end": 556.61, "word": " primary", "probability": 0.93115234375}, {"start": 556.61, "end": 556.95, "word": " source.", "probability": 0.7958984375}, {"start": 557.05, "end": 557.17, "word": " So", "probability": 0.9560546875}, {"start": 557.17, "end": 557.33, "word": " you", "probability": 0.84912109375}, {"start": 557.33, "end": 557.47, "word": " have", "probability": 0.94775390625}, {"start": 557.47, "end": 557.59, "word": " to", "probability": 0.97216796875}, {"start": 557.59, "end": 557.99, "word": " distinguish", "probability": 0.8779296875}, {"start": 557.99, "end": 558.67, "word": " between", "probability": 0.8759765625}, {"start": 558.67, "end": 559.67, "word": " a", "probability": 0.65478515625}, {"start": 559.67, "end": 560.01, "word": " primary", "probability": 0.9306640625}, {"start": 560.01, "end": 560.73, "word": " and", "probability": 0.9443359375}, {"start": 560.73, "end": 561.41, "word": " secondary", "probability": 0.92041015625}, {"start": 561.41, "end": 562.27, "word": " sources.", "probability": 0.740234375}, {"start": 563.11, "end": 563.49, "word": " Any", "probability": 0.892578125}, {"start": 563.49, "end": 563.89, "word": " question?", "probability": 0.71533203125}, {"start": 565.27, "end": 565.83, "word": " Comments?", "probability": 0.92236328125}, {"start": 568.11, "end": 568.81, "word": " Next.", "probability": 0.8896484375}], "temperature": 1.0}, {"id": 21, "seek": 59614, "start": 571.46, "end": 596.14, "text": " We'll talk a little bit about types of variables. In general, there are two types of variables. One is called categorical variables or qualitative variables, and the other one is called numerical or quantitative variables. Now, for example, if I ask you, what's your favorite color? 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Do you like it? Either yes or no, and so on. As I mentioned before, gender, marital status, race, religions, these are examples of qualitative or categorical variables. The other type of variable which is commonly used is called numerical or quantitative data.", "tokens": [1144, 291, 411, 11532, 316, 11, 337, 1365, 11, 2035, 702, 3595, 307, 30, 1144, 291, 411, 309, 30, 13746, 2086, 420, 572, 11, 293, 370, 322, 13, 1018, 286, 2835, 949, 11, 7898, 11, 1849, 1686, 6558, 11, 4569, 11, 21212, 11, 613, 366, 5110, 295, 31312, 420, 19250, 804, 9102, 13, 440, 661, 2010, 295, 7006, 597, 307, 12719, 1143, 307, 1219, 29054, 420, 27778, 1412, 13], "avg_logprob": -0.1277901719723429, "compression_ratio": 1.5260663507109005, "no_speech_prob": 0.0, "words": [{"start": 625.5, "end": 625.88, "word": " Do", "probability": 0.68408203125}, {"start": 625.88, "end": 625.98, "word": " you", "probability": 0.966796875}, {"start": 625.98, "end": 626.2, "word": " like", "probability": 0.94970703125}, {"start": 626.2, "end": 626.68, "word": " candidate", "probability": 0.8134765625}, {"start": 626.68, "end": 627.08, "word": " A,", "probability": 0.83349609375}, {"start": 627.48, 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"start": 651.89, "end": 675.63, "text": " Quantitative variables have values that represent quantities. For example, if I ask you, what's your age? My age is 20 years old or 18 years old. What's your weight? Income. Height? Temperature? Income. So it's a number. Weight, maybe my weight is 70 kilograms.", "tokens": [26968, 14275, 9102, 362, 4190, 300, 2906, 22927, 13, 1171, 1365, 11, 498, 286, 1029, 291, 11, 437, 311, 428, 3205, 30, 1222, 3205, 307, 945, 924, 1331, 420, 2443, 924, 1331, 13, 708, 311, 428, 3364, 30, 682, 1102, 13, 634, 397, 30, 34864, 1503, 30, 682, 1102, 13, 407, 309, 311, 257, 1230, 13, 44464, 11, 1310, 452, 3364, 307, 5285, 30690, 13], "avg_logprob": -0.11612216180021112, "compression_ratio": 1.4475138121546962, "no_speech_prob": 0.0, "words": [{"start": 651.89, "end": 652.49, "word": " Quantitative", "probability": 0.969482421875}, {"start": 652.49, "end": 652.93, "word": " variables", "probability": 0.9326171875}, {"start": 652.93, "end": 653.23, "word": " have", "probability": 0.9443359375}, {"start": 653.23, "end": 653.57, "word": " values", "probability": 0.970703125}, {"start": 653.57, "end": 653.87, "word": " that", "probability": 0.939453125}, {"start": 653.87, "end": 654.47, "word": " represent", "probability": 0.83642578125}, {"start": 654.47, "end": 655.13, "word": " quantities.", "probability": 0.94677734375}, {"start": 655.27, "end": 655.37, "word": " For", "probability": 0.96484375}, {"start": 655.37, "end": 655.71, "word": " example,", "probability": 0.97509765625}, {"start": 656.13, "end": 656.35, "word": " if", "probability": 0.95556640625}, {"start": 656.35, "end": 656.49, "word": " I", "probability": 0.9921875}, {"start": 656.49, "end": 656.69, "word": " ask", "probability": 0.923828125}, {"start": 656.69, "end": 656.81, "word": " you,", "probability": 0.95849609375}, {"start": 656.91, "end": 657.05, "word": " what's", "probability": 0.7281494140625}, {"start": 657.05, "end": 657.19, "word": " your", "probability": 0.89794921875}, {"start": 657.19, "end": 657.55, "word": " age?", "probability": 0.951171875}, {"start": 658.61, "end": 659.21, "word": " My", "probability": 0.96240234375}, {"start": 659.21, "end": 659.43, "word": " age", "probability": 0.95947265625}, {"start": 659.43, "end": 659.59, "word": " is", "probability": 0.94775390625}, {"start": 659.59, "end": 659.89, "word": " 20", "probability": 0.6708984375}, {"start": 659.89, "end": 660.19, "word": " years", "probability": 0.9228515625}, {"start": 660.19, "end": 660.47, "word": " old", "probability": 0.91748046875}, {"start": 660.47, "end": 660.65, "word": " or", "probability": 0.728515625}, {"start": 660.65, "end": 660.89, "word": " 18", "probability": 0.90380859375}, {"start": 660.89, "end": 662.17, "word": " years", "probability": 0.86669921875}, {"start": 662.17, "end": 662.45, "word": " old.", "probability": 0.90234375}, {"start": 662.57, "end": 662.95, "word": " What's", "probability": 0.94091796875}, {"start": 662.95, "end": 663.11, "word": " your", "probability": 0.89697265625}, {"start": 663.11, "end": 663.53, "word": " weight?", "probability": 0.91455078125}, {"start": 664.27, "end": 664.77, "word": " Income.", "probability": 0.966552734375}, {"start": 667.51, "end": 668.11, "word": " Height?", "probability": 0.936279296875}, {"start": 668.53, "end": 669.13, "word": " Temperature?", "probability": 0.97705078125}, {"start": 670.29, "end": 670.89, "word": " Income.", "probability": 0.961181640625}, {"start": 671.01, "end": 671.15, "word": " So", "probability": 0.9296875}, {"start": 671.15, "end": 671.43, "word": " it's", "probability": 0.91259765625}, {"start": 671.43, "end": 672.21, "word": " a", "probability": 0.6767578125}, {"start": 672.21, "end": 672.55, "word": " number.", "probability": 0.93408203125}, {"start": 673.61, "end": 673.87, "word": " Weight,", "probability": 0.8994140625}, {"start": 673.95, "end": 674.07, "word": " maybe", "probability": 0.9423828125}, {"start": 674.07, "end": 674.29, "word": " my", "probability": 0.9560546875}, {"start": 674.29, "end": 674.51, "word": " weight", "probability": 0.93115234375}, {"start": 674.51, "end": 674.75, "word": " is", "probability": 0.9453125}, {"start": 674.75, "end": 675.21, "word": " 70", "probability": 0.96435546875}, {"start": 675.21, "end": 675.63, "word": " kilograms.", "probability": 0.8173828125}], "temperature": 1.0}, {"id": 25, "seek": 70611, "start": 677.41, "end": 706.11, "text": " So weight, age, height, salary, income, number of students, number of phone calls you received on your cell phone during one hour, number of accidents happened in street and so on. So that's the difference between numerical variables and qualitative variables. Anyone of you just give me one example of qualitative and quantitative variables.", "tokens": [407, 3364, 11, 3205, 11, 6681, 11, 15360, 11, 5742, 11, 1230, 295, 1731, 11, 1230, 295, 2593, 5498, 291, 4613, 322, 428, 2815, 2593, 1830, 472, 1773, 11, 1230, 295, 23875, 2011, 294, 4838, 293, 370, 322, 13, 407, 300, 311, 264, 2649, 1296, 29054, 9102, 293, 31312, 9102, 13, 14643, 295, 291, 445, 976, 385, 472, 1365, 295, 31312, 293, 27778, 9102, 13], "avg_logprob": -0.12606533752246338, "compression_ratio": 1.7411167512690355, "no_speech_prob": 0.0, "words": [{"start": 677.41, "end": 678.03, "word": " So", "probability": 0.82958984375}, {"start": 678.03, "end": 678.67, "word": " weight,", "probability": 0.82421875}, {"start": 679.25, "end": 680.25, "word": " age,", "probability": 0.9140625}, {"start": 680.51, "end": 680.91, "word": " height,", "probability": 0.97021484375}, {"start": 681.17, "end": 681.49, "word": " salary,", "probability": 0.958984375}, {"start": 681.77, "end": 681.99, 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"seek": 73506, "start": 707.4, "end": 735.06, "text": " Another examples. Just give me one example for qualitative data. Qualitative or quantitative. Political party, either party A or party B. So suppose there are two parties, so I like party A, she likes party B and so on. So party in this case is qualitative variable, another one.", "tokens": [3996, 5110, 13, 1449, 976, 385, 472, 1365, 337, 31312, 1412, 13, 13616, 14275, 420, 27778, 13, 34265, 3595, 11, 2139, 3595, 316, 420, 3595, 363, 13, 407, 7297, 456, 366, 732, 8265, 11, 370, 286, 411, 3595, 316, 11, 750, 5902, 3595, 363, 293, 370, 322, 13, 407, 3595, 294, 341, 1389, 307, 31312, 7006, 11, 1071, 472, 13], "avg_logprob": -0.17482069672131148, "compression_ratio": 1.6766467065868262, "no_speech_prob": 0.0, "words": [{"start": 707.4, "end": 707.78, "word": " Another", "probability": 0.603515625}, {"start": 707.78, "end": 708.28, "word": " examples.", "probability": 0.74951171875}, {"start": 709.78, "end": 710.34, "word": " Just", "probability": 0.84619140625}, {"start": 710.34, "end": 710.48, "word": " give", "probability": 0.8798828125}, {"start": 710.48, "end": 710.56, "word": " me", "probability": 0.95068359375}, {"start": 710.56, "end": 710.72, "word": " one", "probability": 0.9326171875}, {"start": 710.72, "end": 711.04, "word": " example", "probability": 0.97265625}, {"start": 711.04, "end": 711.26, "word": " for", "probability": 0.94775390625}, {"start": 711.26, "end": 711.7, "word": " qualitative", "probability": 0.81640625}, {"start": 711.7, "end": 712.16, "word": " data.", "probability": 0.93212890625}, {"start": 716.9, "end": 717.46, "word": " Qualitative", "probability": 0.967529296875}, {"start": 717.46, "end": 718.3, "word": " or", "probability": 0.93408203125}, {"start": 718.3, "end": 718.78, "word": " quantitative.", "probability": 0.93359375}, {"start": 721.38, "end": 721.94, "word": " Political", "probability": 0.2337646484375}, {"start": 721.94, "end": 722.34, "word": " party,", "probability": 0.5751953125}, {"start": 722.44, "end": 722.66, "word": " either", "probability": 0.83935546875}, {"start": 722.66, "end": 723.28, "word": " party", "probability": 0.7578125}, {"start": 723.28, "end": 723.52, "word": " A", "probability": 0.93310546875}, {"start": 723.52, "end": 723.72, "word": " or", "probability": 0.9716796875}, {"start": 723.72, "end": 724.04, "word": " party", "probability": 0.87548828125}, {"start": 724.04, "end": 724.26, "word": " B.", "probability": 0.998046875}, {"start": 724.7, "end": 724.88, "word": " So", "probability": 0.642578125}, {"start": 724.88, "end": 725.16, "word": " suppose", "probability": 0.88330078125}, {"start": 725.16, "end": 725.34, "word": " there", "probability": 0.89599609375}, {"start": 725.34, "end": 725.48, "word": " are", "probability": 0.943359375}, {"start": 725.48, "end": 725.7, "word": " two", "probability": 0.93603515625}, {"start": 725.7, "end": 726.06, "word": " parties,", "probability": 0.97607421875}, {"start": 726.26, "end": 726.4, "word": " so", "probability": 0.92041015625}, {"start": 726.4, "end": 727.14, "word": " I", "probability": 0.99609375}, {"start": 727.14, "end": 727.58, "word": " like", "probability": 0.94677734375}, {"start": 727.58, "end": 728.08, "word": " party", "probability": 0.88037109375}, {"start": 728.08, "end": 728.32, "word": " A,", "probability": 0.994140625}, {"start": 728.72, "end": 728.9, "word": " she", "probability": 0.91455078125}, {"start": 728.9, "end": 729.18, "word": " likes", "probability": 0.861328125}, {"start": 729.18, "end": 729.54, "word": " party", "probability": 0.892578125}, {"start": 729.54, "end": 729.68, "word": " B", "probability": 0.99755859375}, {"start": 729.68, "end": 729.84, "word": " and", "probability": 0.4619140625}, {"start": 729.84, "end": 730.0, "word": " so", "probability": 0.9541015625}, {"start": 730.0, "end": 730.2, "word": " on.", "probability": 0.9482421875}, {"start": 730.42, "end": 730.6, "word": " So", "probability": 0.93359375}, {"start": 730.6, "end": 730.92, "word": " party", "probability": 0.88525390625}, {"start": 730.92, "end": 731.88, "word": " in", "probability": 0.48046875}, {"start": 731.88, "end": 732.08, "word": " this", "probability": 0.94775390625}, {"start": 732.08, "end": 732.32, "word": " case", "probability": 0.90185546875}, {"start": 732.32, "end": 732.58, "word": " is", "probability": 0.88037109375}, {"start": 732.58, "end": 733.02, "word": " qualitative", "probability": 0.8046875}, {"start": 733.02, "end": 733.88, "word": " variable,", "probability": 0.9208984375}, {"start": 734.48, "end": 734.76, "word": " another", "probability": 0.9248046875}, {"start": 734.76, "end": 735.06, "word": " one.", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 27, "seek": 77284, "start": 745.4, "end": 772.84, "text": " So types of courses, maybe business, economics, administration, and so on. So types of courses. Another example for quantitative variable or numerical variables. So production is a numerical variable. Another example for quantitative.", "tokens": [407, 3467, 295, 7712, 11, 1310, 1606, 11, 14564, 11, 7236, 11, 293, 370, 322, 13, 407, 3467, 295, 7712, 13, 3996, 1365, 337, 27778, 7006, 420, 29054, 9102, 13, 407, 4265, 307, 257, 29054, 7006, 13, 3996, 1365, 337, 27778, 13], "avg_logprob": -0.17796148047890775, "compression_ratio": 1.7803030303030303, "no_speech_prob": 0.0, "words": [{"start": 745.4, "end": 745.72, "word": " So", "probability": 0.7265625}, {"start": 745.72, "end": 746.14, "word": " types", "probability": 0.67578125}, {"start": 746.14, "end": 746.78, "word": " of", "probability": 0.97119140625}, {"start": 746.78, "end": 747.1, "word": " courses,", "probability": 0.884765625}, {"start": 747.36, "end": 747.52, "word": " maybe", "probability": 0.9033203125}, {"start": 747.52, "end": 748.12, "word": " business,", "probability": 0.81298828125}, {"start": 748.34, "end": 748.82, "word": " economics,", "probability": 0.86376953125}, {"start": 749.48, "end": 750.1, "word": " administration,", "probability": 0.921875}, {"start": 750.44, "end": 751.04, "word": " and", "probability": 0.93701171875}, {"start": 751.04, "end": 751.28, "word": " so", "probability": 0.95556640625}, {"start": 751.28, "end": 751.54, "word": " on.", "probability": 0.95068359375}, {"start": 752.12, "end": 752.28, "word": " So", "probability": 0.88037109375}, {"start": 752.28, "end": 752.62, "word": " types", "probability": 0.7958984375}, {"start": 752.62, "end": 752.88, "word": " of", "probability": 0.97216796875}, {"start": 752.88, "end": 753.26, "word": " courses.", "probability": 0.8916015625}, {"start": 754.26, "end": 754.62, "word": " Another", "probability": 0.869140625}, {"start": 754.62, "end": 755.06, "word": " example", "probability": 0.97509765625}, {"start": 755.06, "end": 755.38, "word": " for", "probability": 0.87939453125}, {"start": 755.38, "end": 755.88, "word": " quantitative", "probability": 0.58349609375}, {"start": 755.88, "end": 756.38, "word": " variable", "probability": 0.89306640625}, {"start": 756.38, "end": 756.6, "word": " or", "probability": 0.83349609375}, {"start": 756.6, "end": 757.1, "word": " numerical", "probability": 0.91357421875}, {"start": 757.1, "end": 757.6, "word": " variables.", "probability": 0.8623046875}, {"start": 765.02, "end": 765.9, "word": " So", "probability": 0.30029296875}, {"start": 765.9, "end": 768.1, "word": " production", "probability": 0.94287109375}, {"start": 768.1, "end": 768.98, "word": " is", "probability": 0.90673828125}, {"start": 768.98, "end": 769.12, "word": " a", "probability": 0.7724609375}, {"start": 769.12, "end": 769.4, "word": " numerical", "probability": 0.9521484375}, {"start": 769.4, "end": 769.82, "word": " variable.", "probability": 0.91015625}, {"start": 770.9, "end": 771.44, "word": " Another", "probability": 0.8837890625}, {"start": 771.44, "end": 771.9, "word": " example", "probability": 0.97265625}, {"start": 771.9, "end": 772.4, "word": " for", "probability": 0.85986328125}, {"start": 772.4, "end": 772.84, "word": " quantitative.", "probability": 0.85205078125}], "temperature": 1.0}, {"id": 28, "seek": 79641, "start": 776.35, "end": 796.41, "text": " Is that produced by this company? Number of cell phones, maybe 20, 17, and so on. Any question? Next. So generally speaking, types of data, data has two types, categorical and numerical data.", "tokens": [1119, 300, 7126, 538, 341, 2237, 30, 5118, 295, 2815, 10216, 11, 1310, 945, 11, 3282, 11, 293, 370, 322, 13, 2639, 1168, 30, 3087, 13, 407, 5101, 4124, 11, 3467, 295, 1412, 11, 1412, 575, 732, 3467, 11, 19250, 804, 293, 29054, 1412, 13], "avg_logprob": -0.23692255434782608, "compression_ratio": 1.2972972972972974, "no_speech_prob": 0.0, "words": [{"start": 776.35, "end": 776.43, "word": " Is", "probability": 0.1485595703125}, {"start": 776.43, "end": 776.55, "word": " that", "probability": 0.73876953125}, {"start": 776.55, "end": 776.89, "word": " produced", "probability": 0.81884765625}, {"start": 776.89, "end": 777.23, "word": " by", "probability": 0.97021484375}, {"start": 777.23, "end": 777.53, "word": " this", "probability": 0.89208984375}, {"start": 777.53, "end": 777.97, "word": " company?", "probability": 0.89697265625}, {"start": 778.31, "end": 778.57, "word": " Number", "probability": 0.77734375}, {"start": 778.57, "end": 778.75, "word": " of", "probability": 0.96826171875}, {"start": 778.75, "end": 778.97, "word": " cell", "probability": 0.89013671875}, {"start": 778.97, "end": 779.17, "word": " phones,", "probability": 0.69189453125}, {"start": 779.27, "end": 779.35, "word": " maybe", "probability": 0.83349609375}, {"start": 779.35, "end": 779.79, "word": " 20,", "probability": 0.83935546875}, {"start": 780.03, "end": 780.69, "word": " 17,", "probability": 0.84912109375}, {"start": 780.81, "end": 781.01, "word": " and", "probability": 0.939453125}, {"start": 781.01, "end": 781.21, "word": " so", "probability": 0.9541015625}, {"start": 781.21, "end": 781.45, "word": " on.", "probability": 0.94873046875}, {"start": 783.23, "end": 783.59, "word": " Any", "probability": 0.89111328125}, {"start": 783.59, "end": 783.95, "word": " question?", "probability": 0.77880859375}, {"start": 786.19, "end": 786.87, "word": " Next.", "probability": 0.92333984375}, {"start": 789.07, "end": 789.61, "word": " So", "probability": 0.8984375}, {"start": 789.61, "end": 789.99, "word": " generally", "probability": 0.751953125}, {"start": 789.99, "end": 790.45, "word": " speaking,", "probability": 0.865234375}, {"start": 790.65, "end": 790.89, "word": " types", "probability": 0.82861328125}, {"start": 790.89, "end": 791.07, "word": " of", "probability": 0.97216796875}, {"start": 791.07, "end": 791.43, "word": " data,", "probability": 0.93701171875}, {"start": 792.05, "end": 792.41, "word": " data", "probability": 0.8447265625}, {"start": 792.41, "end": 792.71, "word": " has", "probability": 0.91650390625}, {"start": 792.71, "end": 792.89, "word": " two", "probability": 0.90234375}, {"start": 792.89, "end": 793.33, "word": " types,", "probability": 0.8310546875}, {"start": 794.09, "end": 794.57, "word": " categorical", "probability": 0.6741943359375}, {"start": 794.57, "end": 795.49, "word": " and", "probability": 0.9189453125}, {"start": 795.49, "end": 795.85, "word": " numerical", "probability": 0.8193359375}, {"start": 795.85, "end": 796.41, "word": " data.", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 29, "seek": 81704, "start": 797.6, "end": 817.04, "text": " As we mentioned, marital status, political party, eye color, and so on. These are examples of categorical variables. On the other hand, a numerical variable can be split or divided into two parts. One is called discrete and the other is continuous, and we have to distinguish between these two. For example,", "tokens": [1018, 321, 2835, 11, 1849, 1686, 6558, 11, 3905, 3595, 11, 3313, 2017, 11, 293, 370, 322, 13, 1981, 366, 5110, 295, 19250, 804, 9102, 13, 1282, 264, 661, 1011, 11, 257, 29054, 7006, 393, 312, 7472, 420, 6666, 666, 732, 3166, 13, 1485, 307, 1219, 27706, 293, 264, 661, 307, 10957, 11, 293, 321, 362, 281, 20206, 1296, 613, 732, 13, 1171, 1365, 11], "avg_logprob": -0.16785037336927472, "compression_ratio": 1.5876288659793814, "no_speech_prob": 0.0, "words": [{"start": 797.6, "end": 797.96, "word": " As", "probability": 0.88720703125}, {"start": 797.96, "end": 798.08, "word": " we", "probability": 0.94775390625}, {"start": 798.08, "end": 798.5, "word": " mentioned,", "probability": 0.81982421875}, {"start": 798.9, "end": 799.18, "word": " marital", "probability": 0.935302734375}, {"start": 799.18, "end": 799.64, "word": " status,", "probability": 0.9384765625}, {"start": 799.94, "end": 800.28, "word": " political", "probability": 0.919921875}, {"start": 800.28, "end": 800.86, "word": " party,", "probability": 0.8876953125}, {"start": 801.02, "end": 801.24, "word": " eye", "probability": 0.8984375}, {"start": 801.24, "end": 801.44, "word": " color,", "probability": 0.61865234375}, {"start": 801.6, "end": 801.72, "word": " and", "probability": 0.93017578125}, {"start": 801.72, "end": 801.92, "word": " so", "probability": 0.95361328125}, {"start": 801.92, "end": 802.18, "word": " on.", "probability": 0.9482421875}, {"start": 802.9, "end": 803.42, "word": " These", "probability": 0.92138671875}, {"start": 803.42, "end": 804.38, "word": " are", "probability": 0.93994140625}, {"start": 804.38, "end": 804.86, "word": " examples", "probability": 0.8544921875}, {"start": 804.86, "end": 805.12, "word": " of", "probability": 0.9697265625}, {"start": 805.12, "end": 805.64, "word": " categorical", "probability": 0.95751953125}, {"start": 805.64, "end": 806.1, "word": " variables.", "probability": 0.93798828125}, {"start": 807.08, "end": 807.5, "word": " On", "probability": 0.95458984375}, {"start": 807.5, "end": 807.62, "word": " the", "probability": 0.923828125}, {"start": 807.62, "end": 807.82, "word": " other", "probability": 0.8828125}, {"start": 807.82, "end": 808.06, "word": " hand,", "probability": 0.9150390625}, {"start": 808.1, "end": 808.18, "word": " a", "probability": 0.51513671875}, {"start": 808.18, "end": 808.46, "word": " numerical", "probability": 0.9580078125}, {"start": 808.46, "end": 808.84, "word": " variable", "probability": 0.89501953125}, {"start": 808.84, "end": 809.1, "word": " can", "probability": 0.94482421875}, {"start": 809.1, "end": 809.3, "word": " be", "probability": 0.95458984375}, {"start": 809.3, "end": 809.64, "word": " split", "probability": 0.54345703125}, {"start": 809.64, "end": 810.0, "word": " or", "probability": 0.80615234375}, {"start": 810.0, "end": 810.46, "word": " divided", "probability": 0.75634765625}, {"start": 810.46, "end": 810.72, "word": " into", "probability": 0.84814453125}, {"start": 810.72, "end": 810.9, "word": " two", "probability": 0.9130859375}, {"start": 810.9, "end": 811.28, "word": " parts.", "probability": 0.86376953125}, {"start": 811.42, "end": 811.54, "word": " One", "probability": 0.9267578125}, {"start": 811.54, "end": 811.74, "word": " is", "probability": 0.9326171875}, {"start": 811.74, "end": 812.2, "word": " called", "probability": 0.9033203125}, {"start": 812.2, "end": 813.26, "word": " discrete", "probability": 0.9287109375}, {"start": 813.26, "end": 813.6, "word": " and", "probability": 0.75537109375}, {"start": 813.6, "end": 813.68, "word": " the", "probability": 0.36181640625}, {"start": 813.68, "end": 813.84, "word": " other", "probability": 0.8330078125}, {"start": 813.84, "end": 814.02, "word": " is", "probability": 0.89404296875}, {"start": 814.02, "end": 814.36, "word": " continuous,", "probability": 0.8359375}, {"start": 814.54, "end": 814.64, "word": " and", "probability": 0.9306640625}, {"start": 814.64, "end": 814.76, "word": " we", "probability": 0.94189453125}, {"start": 814.76, "end": 814.9, "word": " have", "probability": 0.939453125}, {"start": 814.9, "end": 815.02, "word": " to", "probability": 0.95361328125}, {"start": 815.02, "end": 815.32, "word": " distinguish", "probability": 0.765625}, {"start": 815.32, "end": 815.68, "word": " between", "probability": 0.85400390625}, {"start": 815.68, "end": 815.94, "word": " these", "probability": 0.85400390625}, {"start": 815.94, "end": 816.16, "word": " two.", "probability": 0.9365234375}, {"start": 816.52, "end": 816.72, "word": " For", "probability": 0.96337890625}, {"start": 816.72, "end": 817.04, "word": " example,", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 30, "seek": 84442, "start": 818.98, "end": 844.42, "text": " Number of students in this class, you can say there are 60 or 50 students in this class. You cannot say there are 50.5 students. So number of students is discrete because it takes only integers. While for continuous type of numerical variables, you can say that my weight is 80.5 kilograms.", "tokens": [5118, 295, 1731, 294, 341, 1508, 11, 291, 393, 584, 456, 366, 4060, 420, 2625, 1731, 294, 341, 1508, 13, 509, 2644, 584, 456, 366, 2625, 13, 20, 1731, 13, 407, 1230, 295, 1731, 307, 27706, 570, 309, 2516, 787, 41674, 13, 3987, 337, 10957, 2010, 295, 29054, 9102, 11, 291, 393, 584, 300, 452, 3364, 307, 4688, 13, 20, 30690, 13], "avg_logprob": -0.11693948625572144, "compression_ratio": 1.6820809248554913, "no_speech_prob": 0.0, "words": [{"start": 818.98, "end": 819.36, "word": " Number", "probability": 0.498779296875}, {"start": 819.36, "end": 819.54, "word": " of", "probability": 0.9697265625}, {"start": 819.54, "end": 819.84, "word": " students", "probability": 0.9609375}, {"start": 819.84, "end": 820.04, "word": " in", "probability": 0.9423828125}, {"start": 820.04, "end": 820.24, "word": " this", "probability": 0.947265625}, {"start": 820.24, "end": 820.56, "word": " class,", 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That will be later, inshallah. As we mentioned last time, at the end of each chapter, there is a section or sections, sometimes there are two sections, talks about computer programs. 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It's called Computer and Data Analysis or SPSS course. So we are going to skip the computer programs used for any chapters in this book. And that's the end of chapter number three. Any questions? 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Chapter three maybe is the easiest chapter in this book. It's straightforward. We have some formulas to compute some statistical measures.", "tokens": [2661, 322, 7187, 1045, 13, 18874, 1045, 1310, 307, 264, 12889, 7187, 294, 341, 1446, 13, 467, 311, 15325, 13, 492, 362, 512, 30546, 281, 14722, 512, 22820, 8000, 13], "avg_logprob": -0.23198084004463687, "compression_ratio": 1.3636363636363635, "no_speech_prob": 0.0, "words": [{"start": 980.71, "end": 981.19, "word": " quickly", "probability": 0.44580078125}, {"start": 981.19, "end": 981.99, "word": " on", "probability": 0.662109375}, {"start": 981.99, "end": 982.21, "word": " chapter", "probability": 0.51953125}, {"start": 982.21, "end": 982.55, "word": " three.", "probability": 0.66650390625}, {"start": 991.29, "end": 992.21, "word": " Chapter", "probability": 0.8759765625}, {"start": 992.21, "end": 992.59, "word": " three", "probability": 0.716796875}, {"start": 992.59, "end": 993.73, "word": " maybe", "probability": 0.68701171875}, {"start": 993.73, "end": 994.33, "word": " is", "probability": 0.896484375}, {"start": 994.33, "end": 994.49, "word": " the", "probability": 0.92041015625}, {"start": 994.49, "end": 994.75, "word": " easiest", "probability": 0.87744140625}, {"start": 994.75, "end": 995.21, "word": " chapter", "probability": 0.8896484375}, {"start": 995.21, "end": 995.37, "word": " in", "probability": 0.91162109375}, {"start": 995.37, "end": 995.53, "word": " this", "probability": 0.86865234375}, {"start": 995.53, "end": 995.85, "word": " book.", "probability": 0.9775390625}, {"start": 996.69, "end": 996.91, "word": " It's", "probability": 0.66259765625}, {"start": 996.91, "end": 997.37, "word": " straightforward.", "probability": 0.70166015625}, {"start": 997.93, "end": 998.21, "word": " We", "probability": 0.95947265625}, {"start": 998.21, "end": 998.41, "word": " have", "probability": 0.9482421875}, {"start": 998.41, "end": 998.89, "word": " some", "probability": 0.8994140625}, {"start": 998.89, "end": 999.95, "word": " formulas", "probability": 0.9755859375}, {"start": 999.95, "end": 1001.63, "word": " to", "probability": 0.91455078125}, {"start": 1001.63, "end": 1002.03, "word": " compute", "probability": 0.9150390625}, {"start": 1002.03, "end": 1002.51, "word": " some", "probability": 0.8955078125}, {"start": 1002.51, "end": 1003.23, "word": " statistical", "probability": 0.9013671875}, {"start": 1003.23, "end": 1003.79, "word": " measures.", "probability": 0.8466796875}], "temperature": 1.0}, {"id": 37, "seek": 103188, "start": 1004.72, "end": 1031.88, "text": " And we should know how can we calculate these measures and what are the meaning of your results. So chapter three talks about numerical descriptive measures. 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Later, we'll talk about the variation, or spread, or dispersion, and the shape in numerical data. So that's part number one. 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So we have to calculate these measures for the sample. And if we have the entire population, we can compute these measures also for that population. Then I will introduce in more details about something called Paxiplot. How can we construct and interpret a Paxiplot? 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What's the meaning of your result? And later in chapter 11, we'll talk in more details about correlation and regression. So these are the objectives of this chapter. There are some basic definitions before we start. One is called central tendency. 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So the central tendency, in this case, the data values grouped around a typical or central value. Is it clear? So we have data set, large data set. 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Next is the variation, which is the amount of dispersion. Variation is the amount of dispersion or scattering of values. And we'll use, for example, range, variance or standard deviation in order to compute the variation. 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So the shape is the pattern of distribution of values from the lowest value to the highest. So that's the three definitions we need to know before we start. So we'll start with the easiest one, measures of central tendency. 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And our goal or we have two goals actually. We have to know how to compute these measures. Number two, which one is better? The mean or the median or the moon? 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So often we use the mean. And the mean is just sum of the values divided by the sample size. So it's straightforward. We have, for example, three data points. And your goal is to find the average or the mean of these points.", "tokens": [1610, 294, 2674, 11, 445, 584, 264, 914, 13, 407, 2049, 321, 764, 264, 914, 13, 400, 264, 914, 307, 445, 2408, 295, 264, 4190, 6666, 538, 264, 6889, 2744, 13, 407, 309, 311, 15325, 13, 492, 362, 11, 337, 1365, 11, 1045, 1412, 2793, 13, 400, 428, 3387, 307, 281, 915, 264, 4274, 420, 264, 914, 295, 613, 2793, 13], "avg_logprob": -0.1500756000318835, "compression_ratio": 1.5696969696969696, "no_speech_prob": 0.0, "words": [{"start": 1275.68, "end": 1276.04, "word": " Or", "probability": 0.287109375}, {"start": 1276.04, "end": 1276.86, "word": " in", "probability": 0.86572265625}, {"start": 1276.86, "end": 1277.22, "word": " general,", "probability": 0.9072265625}, {"start": 1277.4, "end": 1277.6, "word": " just", "probability": 0.9091796875}, {"start": 1277.6, "end": 1278.06, "word": " say", "probability": 0.94384765625}, {"start": 1278.06, "end": 1278.64, "word": " the", "probability": 0.7998046875}, {"start": 1278.64, "end": 1278.82, "word": " mean.", "probability": 0.96923828125}, {"start": 1279.06, "end": 1279.18, "word": " So", "probability": 0.9599609375}, {"start": 1279.18, "end": 1279.48, "word": " often", "probability": 0.78759765625}, {"start": 1279.48, "end": 1279.66, "word": " we", "probability": 0.67529296875}, {"start": 1279.66, "end": 1280.02, "word": " use", "probability": 0.873046875}, {"start": 1280.02, "end": 1280.98, "word": " the", "probability": 0.91015625}, {"start": 1280.98, "end": 1281.18, "word": " mean.", "probability": 0.962890625}, {"start": 1281.68, "end": 1281.86, "word": " And", "probability": 0.7548828125}, {"start": 1281.86, "end": 1282.0, "word": " the", "probability": 0.92333984375}, {"start": 1282.0, "end": 1282.2, "word": " mean", "probability": 0.96826171875}, {"start": 1282.2, "end": 1282.46, "word": " is", "probability": 0.94287109375}, {"start": 1282.46, "end": 1283.36, "word": " just", "probability": 0.89111328125}, {"start": 1283.36, "end": 1286.86, "word": " sum", "probability": 0.5849609375}, {"start": 1286.86, "end": 1287.08, "word": " of", "probability": 0.9619140625}, {"start": 1287.08, "end": 1287.22, "word": " the", "probability": 0.91845703125}, {"start": 1287.22, "end": 1287.66, "word": " values", "probability": 0.97265625}, {"start": 1287.66, "end": 1289.74, "word": " divided", "probability": 0.55224609375}, {"start": 1289.74, "end": 1290.12, "word": " by", "probability": 0.96923828125}, {"start": 1290.12, "end": 1290.8, "word": " the", "probability": 0.92822265625}, {"start": 1290.8, "end": 1291.24, "word": " sample", "probability": 0.8935546875}, {"start": 1291.24, "end": 1291.72, "word": " size.", "probability": 0.86328125}, {"start": 1292.38, "end": 1292.7, "word": " So", "probability": 0.9130859375}, {"start": 1292.7, "end": 1293.22, "word": " it's", "probability": 0.718505859375}, {"start": 1293.22, "end": 1293.7, "word": " straightforward.", "probability": 0.880859375}, {"start": 1294.22, "end": 1294.42, "word": " We", "probability": 0.951171875}, {"start": 1294.42, "end": 1294.68, "word": " have,", "probability": 0.94873046875}, {"start": 1295.14, "end": 1295.22, "word": " for", "probability": 0.94873046875}, {"start": 1295.22, "end": 1295.58, "word": " example,", "probability": 0.974609375}, {"start": 1296.12, "end": 1296.4, "word": " three", "probability": 0.9130859375}, {"start": 1296.4, "end": 1296.8, "word": " data", "probability": 0.9501953125}, {"start": 1296.8, "end": 1297.16, "word": " points.", "probability": 0.88525390625}, {"start": 1298.28, "end": 1298.74, "word": " And", "probability": 0.93408203125}, {"start": 1298.74, "end": 1298.96, "word": " your", "probability": 0.87744140625}, {"start": 1298.96, "end": 1299.18, "word": " goal", "probability": 0.974609375}, {"start": 1299.18, "end": 1299.34, "word": " is", "probability": 0.94580078125}, {"start": 1299.34, "end": 1299.48, "word": " to", "probability": 0.9716796875}, {"start": 1299.48, "end": 1299.88, "word": " find", "probability": 0.8916015625}, {"start": 1299.88, "end": 1301.52, "word": " the", "probability": 0.916015625}, {"start": 1301.52, "end": 1301.9, "word": " average", "probability": 0.83203125}, {"start": 1301.9, "end": 1302.18, "word": " or", "probability": 0.8388671875}, {"start": 1302.18, "end": 1302.34, "word": " the", "probability": 0.9306640625}, {"start": 1302.34, "end": 1302.52, "word": " mean", "probability": 0.97509765625}, {"start": 1302.52, "end": 1302.66, "word": " of", "probability": 0.95947265625}, {"start": 1302.66, "end": 1302.84, "word": " these", "probability": 0.84814453125}, {"start": 1302.84, "end": 1303.24, "word": " points.", "probability": 0.9384765625}], "temperature": 1.0}, {"id": 48, "seek": 133151, "start": 1304.27, "end": 1331.51, "text": " They mean it's just some of these values divided by the sample size. So for example, if we have a data X1, X2, X3 up to Xn. So the average is denoted by X bar. This one is pronounced as X bar and X bar is just sum of Xi. 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So it means X1 plus X2 all the way up to XN divided by N gives the mean or the arithmetic mean. So X bar is the average which is the sum of values divided by the number of observations. So that's the first definition. 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Number two, the definition of the mean. Sum of values divided by the number of values. That means the mean takes all the values, then divided by N.", "tokens": [407, 797, 11, 264, 914, 307, 264, 881, 2689, 3481, 295, 3056, 18187, 13, 5118, 732, 11, 264, 7123, 295, 264, 914, 13, 8626, 295, 4190, 6666, 538, 264, 1230, 295, 4190, 13, 663, 1355, 264, 914, 2516, 439, 264, 4190, 11, 550, 6666, 538, 426, 13], "avg_logprob": -0.17887369574358067, "compression_ratio": 1.5970149253731343, "no_speech_prob": 0.0, "words": [{"start": 1362.18, "end": 1362.42, "word": " So", "probability": 0.82763671875}, {"start": 1362.42, "end": 1362.72, "word": " again,", "probability": 0.8232421875}, {"start": 1364.04, "end": 1364.2, "word": " the", "probability": 0.88916015625}, {"start": 1364.2, "end": 1364.4, "word": " mean", "probability": 0.91943359375}, {"start": 1364.4, "end": 1365.46, "word": " is", "probability": 0.93408203125}, {"start": 1365.46, "end": 1365.68, "word": " the", "probability": 0.923828125}, {"start": 1365.68, "end": 1366.02, "word": " most", "probability": 0.9140625}, {"start": 1366.02, "end": 1366.44, "word": " common", "probability": 0.875}, {"start": 1366.44, "end": 1366.72, "word": " measure", "probability": 0.86865234375}, {"start": 1366.72, "end": 1366.92, "word": " of", "probability": 0.96728515625}, {"start": 1366.92, "end": 1367.18, "word": " center", "probability": 0.5556640625}, {"start": 1367.18, "end": 1367.7, "word": " tendency.", "probability": 0.87744140625}, {"start": 1368.86, "end": 1369.08, "word": " Number", "probability": 0.7451171875}, {"start": 1369.08, "end": 1369.36, "word": " two,", "probability": 0.75}, {"start": 1370.56, "end": 1371.12, "word": " the", "probability": 0.904296875}, {"start": 1371.12, "end": 1371.48, "word": " definition", "probability": 0.9453125}, {"start": 1371.48, "end": 1371.66, "word": " of", "probability": 0.9697265625}, {"start": 1371.66, "end": 1371.78, "word": " the", "probability": 0.9150390625}, {"start": 1371.78, "end": 1371.96, "word": " mean.", "probability": 0.96044921875}, {"start": 1372.92, "end": 1373.34, "word": " Sum", "probability": 0.81884765625}, {"start": 1373.34, "end": 1373.54, "word": " of", "probability": 0.97509765625}, {"start": 1373.54, "end": 1373.92, "word": " values", "probability": 0.96240234375}, {"start": 1373.92, "end": 1374.34, "word": " divided", "probability": 0.791015625}, {"start": 1374.34, "end": 1374.54, "word": " by", "probability": 0.96826171875}, {"start": 1374.54, "end": 1374.72, "word": " the", "probability": 0.89501953125}, {"start": 1374.72, "end": 1374.98, "word": " number", "probability": 0.9326171875}, {"start": 1374.98, "end": 1375.44, "word": " of", "probability": 0.97216796875}, {"start": 1375.44, "end": 1376.94, "word": " values.", "probability": 0.9189453125}, {"start": 1378.38, "end": 1379.06, "word": " That", "probability": 0.89697265625}, {"start": 1379.06, "end": 1379.52, "word": " means", "probability": 0.927734375}, {"start": 1379.52, "end": 1380.16, "word": " the", "probability": 0.6796875}, {"start": 1380.16, "end": 1380.48, "word": " mean", "probability": 0.97705078125}, {"start": 1380.48, "end": 1381.92, "word": " takes", "probability": 0.80029296875}, {"start": 1381.92, "end": 1382.34, "word": " all", "probability": 0.95361328125}, {"start": 1382.34, "end": 1382.5, "word": " the", "probability": 0.91259765625}, {"start": 1382.5, "end": 1382.96, "word": " values,", "probability": 0.96484375}, {"start": 1384.14, "end": 1384.76, "word": " then", "probability": 0.83984375}, {"start": 1384.76, "end": 1385.06, "word": " divided", "probability": 0.347412109375}, {"start": 1385.06, "end": 1385.24, "word": " by", "probability": 0.96875}, {"start": 1385.24, "end": 1385.44, "word": " N.", "probability": 0.485107421875}], "temperature": 1.0}, {"id": 51, "seek": 141556, "start": 1387.02, "end": 1415.56, "text": " it makes sense that the mean is affected by extreme values or outliers. I mean, if the data has outliers or extreme values, I mean by extreme values, large or very, very large values and small, small values. Large values or small values are extreme values. Since the mean takes all these values and sums all together, doesn't divide by n, that means", "tokens": [309, 1669, 2020, 300, 264, 914, 307, 8028, 538, 8084, 4190, 420, 484, 23646, 13, 286, 914, 11, 498, 264, 1412, 575, 484, 23646, 420, 8084, 4190, 11, 286, 914, 538, 8084, 4190, 11, 2416, 420, 588, 11, 588, 2416, 4190, 293, 1359, 11, 1359, 4190, 13, 33092, 4190, 420, 1359, 4190, 366, 8084, 4190, 13, 4162, 264, 914, 2516, 439, 613, 4190, 293, 34499, 439, 1214, 11, 1177, 380, 9845, 538, 297, 11, 300, 1355], "avg_logprob": -0.19399350184898873, "compression_ratio": 1.9553072625698324, "no_speech_prob": 0.0, "words": [{"start": 1387.02, "end": 1387.22, "word": " it", "probability": 0.572265625}, {"start": 1387.22, "end": 1387.6, "word": " makes", "probability": 0.82958984375}, {"start": 1387.6, "end": 1387.96, "word": " sense", "probability": 0.822265625}, {"start": 1387.96, "end": 1388.46, "word": " that", "probability": 0.92626953125}, {"start": 1388.46, "end": 1389.04, "word": " the", 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For example, imagine we have simple data as 1, 2, 3, 4, and 5. Simple example. Now, what's the mean? The mean is just add these values, then divide by the total number of observations. In this case, the sum of these is 15. N is five because there are five observations.", "tokens": [440, 914, 307, 8028, 538, 484, 23646, 420, 538, 8084, 4190, 13, 1171, 1365, 11, 3811, 321, 362, 2199, 1412, 382, 502, 11, 568, 11, 805, 11, 1017, 11, 293, 1025, 13, 21532, 1365, 13, 823, 11, 437, 311, 264, 914, 30, 440, 914, 307, 445, 909, 613, 4190, 11, 550, 9845, 538, 264, 3217, 1230, 295, 18163, 13, 682, 341, 1389, 11, 264, 2408, 295, 613, 307, 2119, 13, 426, 307, 1732, 570, 456, 366, 1732, 18163, 13], "avg_logprob": -0.15595702435821296, "compression_ratio": 1.555023923444976, "no_speech_prob": 0.0, "words": [{"start": 1416.55, "end": 1416.87, "word": " The", "probability": 0.5458984375}, {"start": 1416.87, "end": 1417.01, "word": " mean", "probability": 0.95361328125}, {"start": 1417.01, "end": 1417.15, "word": " is", "probability": 0.9423828125}, {"start": 1417.15, "end": 1417.53, "word": " affected", "probability": 0.81396484375}, {"start": 1417.53, "end": 1418.55, "word": " by", "probability": 0.970703125}, {"start": 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So straightforward. Now imagine instead of 5, this number 5, we have a 10. Now 10, there is a gap between 4, which is the second largest, and the maximum, which is 10. 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There is big change between three and four, around 25% more. 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So take this information in your mind because later we'll talk a little bit about another one. So the mean is affected by extreme values. Imagine another example. Suppose we have data from 1 to 9. 1, 2, 3, 4, 6, 7, 8, 9. 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Imagine the mean was 5, it changed to 14.5. It means around three times. So that means outliers affect the mean much more than the other one. We'll talk a little later about it, which is the median. So keep in mind outliers", "tokens": [1396, 934, 321, 3869, 2319, 11, 309, 3643, 3499, 13, 20, 13, 11739, 264, 914, 390, 1025, 11, 309, 3105, 281, 3499, 13, 20, 13, 467, 1355, 926, 1045, 1413, 13, 407, 300, 1355, 484, 23646, 3345, 264, 914, 709, 544, 813, 264, 661, 472, 13, 492, 603, 751, 257, 707, 1780, 466, 309, 11, 597, 307, 264, 26779, 13, 407, 1066, 294, 1575, 484, 23646], "avg_logprob": -0.19729477878826768, "compression_ratio": 1.52, "no_speech_prob": 0.0, "words": [{"start": 1556.77, "end": 1557.05, "word": " Then", "probability": 0.59423828125}, {"start": 1557.05, "end": 1557.45, "word": " after", "probability": 0.7548828125}, {"start": 1557.45, "end": 1557.61, "word": " we", "probability": 0.94384765625}, {"start": 1557.61, "end": 1557.97, "word": " added", "probability": 0.87060546875}, {"start": 1557.97, "end": 1558.43, "word": " 100,", "probability": 0.728515625}, {"start": 1558.65, "end": 1558.85, "word": " it", "probability": 0.953125}, {"start": 1558.85, "end": 1559.35, "word": " becomes", "probability": 0.8505859375}, {"start": 1559.35, "end": 1560.05, "word": " 14", "probability": 0.96923828125}, {"start": 1560.05, "end": 1560.63, "word": ".5.", "probability": 0.99462890625}, {"start": 1560.81, "end": 1561.35, "word": " Imagine", "probability": 0.89599609375}, {"start": 1561.35, "end": 1562.07, "word": " the", "probability": 0.69580078125}, {"start": 1562.07, "end": 1562.25, "word": " mean", "probability": 0.951171875}, {"start": 1562.25, "end": 1562.77, "word": " was", "probability": 0.57470703125}, {"start": 1562.77, "end": 1563.33, "word": " 5,", "probability": 0.66162109375}, {"start": 1564.17, "end": 1564.45, "word": " it", "probability": 0.93212890625}, {"start": 1564.45, "end": 1565.47, "word": " changed", "probability": 0.54833984375}, {"start": 1565.47, "end": 1566.39, "word": " to", "probability": 0.96484375}, {"start": 1566.39, "end": 1568.15, "word": " 14", "probability": 0.95556640625}, {"start": 1568.15, "end": 1568.67, "word": ".5.", "probability": 0.99853515625}, {"start": 1568.73, "end": 1568.89, "word": " It", "probability": 0.845703125}, {"start": 1568.89, "end": 1569.15, "word": " means", "probability": 0.90966796875}, {"start": 1569.15, "end": 1569.43, "word": " around", "probability": 0.9423828125}, {"start": 1569.43, "end": 1569.67, "word": " three", "probability": 0.56982421875}, {"start": 1569.67, "end": 1570.13, "word": " times.", "probability": 0.9208984375}, {"start": 1571.23, "end": 1571.45, "word": " So", "probability": 0.80126953125}, {"start": 1571.45, "end": 1571.65, "word": " that", "probability": 0.88525390625}, {"start": 1571.65, "end": 1572.03, "word": " means", "probability": 0.93505859375}, {"start": 1572.03, "end": 1572.73, "word": " outliers", "probability": 0.909912109375}, {"start": 1572.73, "end": 1574.59, "word": " affect", "probability": 0.92236328125}, {"start": 1574.59, "end": 1574.83, "word": " the", "probability": 0.921875}, {"start": 1574.83, "end": 1575.05, "word": " mean", "probability": 0.970703125}, {"start": 1575.05, "end": 1575.45, "word": " much", "probability": 0.8857421875}, {"start": 1575.45, "end": 1575.75, "word": " more", "probability": 0.9365234375}, {"start": 1575.75, "end": 1576.07, "word": " than", "probability": 0.91064453125}, {"start": 1576.07, "end": 1577.51, "word": " the", "probability": 0.24658203125}, {"start": 1577.51, "end": 1577.83, "word": " other", "probability": 0.86962890625}, {"start": 1577.83, "end": 1578.05, "word": " one.", "probability": 0.8828125}, {"start": 1578.11, "end": 1578.25, "word": " We'll", "probability": 0.814697265625}, {"start": 1578.25, "end": 1578.47, "word": " talk", "probability": 0.89892578125}, {"start": 1578.47, "end": 1578.87, "word": " a", "probability": 0.67919921875}, {"start": 1578.87, "end": 1578.87, "word": " little", "probability": 0.841796875}, {"start": 1578.87, "end": 1579.31, "word": " later", "probability": 0.8828125}, {"start": 1579.31, "end": 1579.69, "word": " about", "probability": 0.90234375}, {"start": 1579.69, "end": 1579.89, "word": " it,", "probability": 0.931640625}, {"start": 1579.99, "end": 1580.05, "word": " which", "probability": 0.94287109375}, {"start": 1580.05, "end": 1580.15, "word": " is", "probability": 0.9423828125}, {"start": 1580.15, "end": 1580.27, "word": " the", "probability": 0.921875}, {"start": 1580.27, "end": 1580.49, "word": " median.", "probability": 0.978515625}, {"start": 1581.11, "end": 1581.45, "word": " So", "probability": 0.9580078125}, {"start": 1581.45, "end": 1582.01, "word": " keep", "probability": 0.8466796875}, {"start": 1582.01, "end": 1582.13, "word": " in", "probability": 0.9443359375}, {"start": 1582.13, "end": 1582.43, "word": " mind", "probability": 0.88720703125}, {"start": 1582.43, "end": 1583.95, "word": " outliers", "probability": 0.775390625}], "temperature": 1.0}, {"id": 58, "seek": 161493, "start": 1585.29, "end": 1614.93, "text": " affected the mean in this case. Any question? Is it clear? Yes. So, one more time. The mean is affected by extreme values. So that's for the mean. The other measure of center tendency is called the median. Now, what's the median?", "tokens": [8028, 264, 914, 294, 341, 1389, 13, 2639, 1168, 30, 1119, 309, 1850, 30, 1079, 13, 407, 11, 472, 544, 565, 13, 440, 914, 307, 8028, 538, 8084, 4190, 13, 407, 300, 311, 337, 264, 914, 13, 440, 661, 3481, 295, 3056, 18187, 307, 1219, 264, 26779, 13, 823, 11, 437, 311, 264, 26779, 30], "avg_logprob": -0.17857143389327185, "compression_ratio": 1.5436241610738255, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1585.29, "end": 1585.91, "word": " affected", "probability": 0.64306640625}, {"start": 1585.91, "end": 1586.49, "word": " the", "probability": 0.81982421875}, {"start": 1586.49, "end": 1586.73, "word": " mean", "probability": 0.96435546875}, {"start": 1586.73, "end": 1588.93, "word": " in", "probability": 0.7490234375}, {"start": 1588.93, "end": 1589.15, "word": " this", "probability": 0.94970703125}, {"start": 1589.15, "end": 1589.51, "word": " case.", "probability": 0.91748046875}, {"start": 1591.81, "end": 1592.09, "word": " Any", "probability": 0.84765625}, {"start": 1592.09, "end": 1592.49, "word": " question?", "probability": 0.6826171875}, {"start": 1594.53, "end": 1594.79, "word": " Is", "probability": 0.79345703125}, {"start": 1594.79, "end": 1594.91, "word": " it", "probability": 0.857421875}, {"start": 1594.91, "end": 1595.19, "word": " clear?", "probability": 0.896484375}, {"start": 1595.51, "end": 1595.73, "word": " Yes.", "probability": 0.373046875}, {"start": 1597.35, "end": 1598.15, "word": " So,", "probability": 0.8740234375}, {"start": 1598.55, "end": 1599.27, "word": " one", "probability": 0.93408203125}, {"start": 1599.27, "end": 1599.45, "word": " more", "probability": 0.93798828125}, {"start": 1599.45, "end": 1599.71, "word": " time.", "probability": 0.8935546875}, {"start": 1600.51, "end": 1600.91, "word": " The", "probability": 0.8828125}, {"start": 1600.91, "end": 1601.15, "word": " mean", "probability": 0.97119140625}, {"start": 1601.15, "end": 1601.59, "word": " is", "probability": 0.9521484375}, {"start": 1601.59, "end": 1602.03, "word": " affected", "probability": 0.8583984375}, {"start": 1602.03, "end": 1602.69, "word": " by", "probability": 0.97265625}, {"start": 1602.69, "end": 1604.17, "word": " extreme", "probability": 0.876953125}, {"start": 1604.17, "end": 1605.17, "word": " values.", "probability": 0.970703125}, {"start": 1605.81, "end": 1606.09, "word": " So", "probability": 0.9462890625}, {"start": 1606.09, "end": 1606.49, "word": " that's", "probability": 0.8076171875}, {"start": 1606.49, "end": 1606.81, "word": " for", "probability": 0.94482421875}, {"start": 1606.81, "end": 1606.99, "word": " the", "probability": 0.92822265625}, {"start": 1606.99, "end": 1607.15, "word": " mean.", "probability": 0.943359375}, {"start": 1608.11, "end": 1608.91, "word": " The", "probability": 0.89208984375}, {"start": 1608.91, "end": 1609.19, "word": " other", "probability": 0.88916015625}, {"start": 1609.19, "end": 1609.47, "word": " measure", "probability": 0.82568359375}, {"start": 1609.47, "end": 1609.75, "word": " of", "probability": 0.96728515625}, {"start": 1609.75, "end": 1610.03, "word": " center", "probability": 0.62255859375}, {"start": 1610.03, "end": 1610.47, "word": " tendency", "probability": 0.445068359375}, {"start": 1610.47, "end": 1610.91, "word": " is", "probability": 0.93994140625}, {"start": 1610.91, "end": 1611.33, "word": " called", "probability": 0.884765625}, {"start": 1611.33, "end": 1611.83, "word": " the", "probability": 0.88623046875}, {"start": 1611.83, "end": 1612.05, "word": " median.", "probability": 0.9169921875}, {"start": 1613.87, "end": 1614.39, "word": " Now,", "probability": 0.94580078125}, {"start": 1614.45, "end": 1614.63, "word": " what's", "probability": 0.928466796875}, {"start": 1614.63, "end": 1614.75, "word": " the", "probability": 0.92333984375}, {"start": 1614.75, "end": 1614.93, "word": " median?", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 59, "seek": 162670, "start": 1617.12, "end": 1626.7, "text": " What's the definition of the median from your previous studies? What's the median? I mean, what's the definition of the median?", "tokens": [708, 311, 264, 7123, 295, 264, 26779, 490, 428, 3894, 5313, 30, 708, 311, 264, 26779, 30, 286, 914, 11, 437, 311, 264, 7123, 295, 264, 26779, 30], "avg_logprob": -0.1697198275862069, "compression_ratio": 1.4883720930232558, "no_speech_prob": 0.0, "words": [{"start": 1617.12, "end": 1617.6, "word": " What's", "probability": 0.752197265625}, {"start": 1617.6, "end": 1617.68, "word": " the", "probability": 0.9287109375}, {"start": 1617.68, "end": 1618.0, "word": " definition", "probability": 0.923828125}, {"start": 1618.0, "end": 1618.22, "word": " of", "probability": 0.96728515625}, {"start": 1618.22, "end": 1618.36, "word": " the", "probability": 0.71044921875}, {"start": 1618.36, "end": 1618.6, "word": " median", "probability": 0.9541015625}, {"start": 1618.6, "end": 1620.12, "word": " from", "probability": 0.37353515625}, {"start": 1620.12, "end": 1620.38, "word": " your", "probability": 0.89453125}, {"start": 1620.38, "end": 1620.76, "word": " previous", "probability": 0.85107421875}, {"start": 1620.76, "end": 1621.24, "word": " studies?", "probability": 0.97265625}, {"start": 1622.22, "end": 1622.46, "word": " What's", "probability": 0.8203125}, {"start": 1622.46, "end": 1622.62, "word": " the", "probability": 0.92919921875}, {"start": 1622.62, "end": 1622.9, "word": " median?", "probability": 0.72802734375}, {"start": 1625.0, "end": 1625.32, "word": " I", "probability": 0.693359375}, {"start": 1625.32, "end": 1625.5, "word": " mean,", "probability": 0.96826171875}, {"start": 1625.58, "end": 1625.76, "word": " what's", "probability": 0.959716796875}, {"start": 1625.76, "end": 1625.88, "word": " the", "probability": 0.92919921875}, {"start": 1625.88, "end": 1626.18, "word": " definition", "probability": 0.94482421875}, {"start": 1626.18, "end": 1626.38, "word": " of", "probability": 0.96875}, {"start": 1626.38, "end": 1626.5, "word": " the", "probability": 0.912109375}, {"start": 1626.5, "end": 1626.7, "word": " median?", "probability": 0.962890625}], "temperature": 1.0}, {"id": 60, "seek": 164802, "start": 1627.86, "end": 1648.02, "text": " Now the middle value, that's correct, but after we arrange the data from smallest to largest or largest to smallest, so we should arrange the data, then we can figure out the median. So the median is the middle point, but after we arrange the data from smallest to largest or vice versa.", "tokens": [823, 264, 2808, 2158, 11, 300, 311, 3006, 11, 457, 934, 321, 9424, 264, 1412, 490, 16998, 281, 6443, 420, 6443, 281, 16998, 11, 370, 321, 820, 9424, 264, 1412, 11, 550, 321, 393, 2573, 484, 264, 26779, 13, 407, 264, 26779, 307, 264, 2808, 935, 11, 457, 934, 321, 9424, 264, 1412, 490, 16998, 281, 6443, 420, 11964, 25650, 13], "avg_logprob": -0.1500756000318835, "compression_ratio": 1.986206896551724, "no_speech_prob": 0.0, "words": [{"start": 1627.86, "end": 1628.22, "word": " Now", "probability": 0.85302734375}, {"start": 1628.22, "end": 1628.68, "word": " the", "probability": 0.4072265625}, {"start": 1628.68, "end": 1628.92, "word": " middle", "probability": 0.8955078125}, {"start": 1628.92, "end": 1629.36, "word": " value,", "probability": 0.97998046875}, {"start": 1629.76, "end": 1630.06, "word": " that's", "probability": 0.910888671875}, {"start": 1630.06, "end": 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"start": 1648.85, "end": 1675.99, "text": " So that's the definition of the median. So in an ordered array, so we have to have order array, the median is the middle number. The middle number means 50 percent of the data below and 50 percent above the median because it's called the median, the value in the middle after you arrange the data from smallest to largest.", "tokens": [407, 300, 311, 264, 7123, 295, 264, 26779, 13, 407, 294, 364, 8866, 10225, 11, 370, 321, 362, 281, 362, 1668, 10225, 11, 264, 26779, 307, 264, 2808, 1230, 13, 440, 2808, 1230, 1355, 2625, 3043, 295, 264, 1412, 2507, 293, 2625, 3043, 3673, 264, 26779, 570, 309, 311, 1219, 264, 26779, 11, 264, 2158, 294, 264, 2808, 934, 291, 9424, 264, 1412, 490, 16998, 281, 6443, 13], "avg_logprob": -0.11967844418857408, "compression_ratio": 1.8044692737430168, "no_speech_prob": 0.0, "words": [{"start": 1648.85, "end": 1649.09, "word": " So", "probability": 0.873046875}, {"start": 1649.09, "end": 1649.33, "word": " that's", "probability": 0.92724609375}, {"start": 1649.33, "end": 1649.43, "word": " the", "probability": 0.8388671875}, {"start": 1649.43, "end": 1649.73, "word": " definition", 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0.64599609375}, {"start": 1672.19, "end": 1672.35, "word": " you", "probability": 0.93505859375}, {"start": 1672.35, "end": 1672.65, "word": " arrange", "probability": 0.77197265625}, {"start": 1672.65, "end": 1672.83, "word": " the", "probability": 0.91357421875}, {"start": 1672.83, "end": 1673.19, "word": " data", "probability": 0.939453125}, {"start": 1673.19, "end": 1674.01, "word": " from", "probability": 0.8818359375}, {"start": 1674.01, "end": 1674.67, "word": " smallest", "probability": 0.943359375}, {"start": 1674.67, "end": 1675.67, "word": " to", "probability": 0.97216796875}, {"start": 1675.67, "end": 1675.99, "word": " largest.", "probability": 0.91845703125}], "temperature": 1.0}, {"id": 62, "seek": 170233, "start": 1680.13, "end": 1702.33, "text": " Suppose I again go back to the previous example when we have data 1, 2, 3, 4, and 5. Now for this specific example as we did before, now the data is already ordered. The value in the middle is 3 because there are two pillows.", "tokens": [21360, 286, 797, 352, 646, 281, 264, 3894, 1365, 562, 321, 362, 1412, 502, 11, 568, 11, 805, 11, 1017, 11, 293, 1025, 13, 823, 337, 341, 2685, 1365, 382, 321, 630, 949, 11, 586, 264, 1412, 307, 1217, 8866, 13, 440, 2158, 294, 264, 2808, 307, 805, 570, 456, 366, 732, 38630, 13], "avg_logprob": -0.20980114069851963, "compression_ratio": 1.3614457831325302, "no_speech_prob": 0.0, "words": [{"start": 1680.13, "end": 1680.65, "word": " Suppose", "probability": 0.79150390625}, {"start": 1680.65, "end": 1681.13, "word": " I", "probability": 0.5654296875}, {"start": 1681.13, "end": 1681.35, "word": " again", "probability": 0.468994140625}, {"start": 1681.35, "end": 1681.51, "word": " go", "probability": 0.8779296875}, {"start": 1681.51, "end": 1681.75, "word": " back", "probability": 0.8740234375}, {"start": 1681.75, "end": 1681.89, "word": " to", "probability": 0.96923828125}, {"start": 1681.89, "end": 1682.03, "word": " the", "probability": 0.92041015625}, {"start": 1682.03, "end": 1682.27, "word": " previous", "probability": 0.86474609375}, {"start": 1682.27, "end": 1682.77, "word": " example", "probability": 0.97509765625}, {"start": 1682.77, "end": 1683.03, "word": " when", "probability": 0.50830078125}, {"start": 1683.03, "end": 1683.19, "word": " we", "probability": 0.9619140625}, {"start": 1683.19, "end": 1683.59, "word": " have", "probability": 0.93798828125}, {"start": 1683.59, "end": 1684.49, "word": " data", "probability": 0.875}, {"start": 1684.49, "end": 1684.95, "word": " 1,", "probability": 0.480712890625}, {"start": 1685.01, "end": 1685.13, "word": " 2,", "probability": 0.89794921875}, {"start": 1685.23, "end": 1685.37, "word": " 3,", "probability": 0.9931640625}, {"start": 1685.47, "end": 1685.63, "word": " 4,", "probability": 0.99609375}, {"start": 1685.65, "end": 1685.79, "word": " and", "probability": 0.89306640625}, {"start": 1685.79, "end": 1686.13, "word": " 5.", "probability": 0.9970703125}, {"start": 1688.63, "end": 1689.15, "word": " Now", "probability": 0.93798828125}, {"start": 1689.15, "end": 1689.39, "word": " for", "probability": 0.59033203125}, {"start": 1689.39, "end": 1689.69, "word": " this", "probability": 0.94873046875}, {"start": 1689.69, "end": 1690.25, "word": " specific", "probability": 0.904296875}, {"start": 1690.25, "end": 1690.79, "word": " example", "probability": 0.974609375}, {"start": 1690.79, "end": 1691.09, "word": " as", "probability": 0.56689453125}, {"start": 1691.09, "end": 1691.29, "word": " we", "probability": 0.96435546875}, {"start": 1691.29, "end": 1691.57, "word": " did", "probability": 0.962890625}, {"start": 1691.57, "end": 1692.03, "word": " before,", "probability": 0.87109375}, {"start": 1692.77, "end": 1693.13, "word": " now", "probability": 0.76611328125}, {"start": 1693.13, "end": 1693.33, "word": " the", "probability": 0.892578125}, {"start": 1693.33, "end": 1693.99, "word": " data", "probability": 0.8515625}, {"start": 1693.99, "end": 1694.21, "word": " is", "probability": 0.9287109375}, {"start": 1694.21, "end": 1694.57, "word": " already", "probability": 0.94384765625}, {"start": 1694.57, "end": 1696.05, "word": " ordered.", "probability": 0.7373046875}, {"start": 1697.09, "end": 1697.61, "word": " The", "probability": 0.89306640625}, {"start": 1697.61, "end": 1697.83, "word": " value", "probability": 0.9814453125}, {"start": 1697.83, "end": 1697.95, "word": " in", "probability": 0.802734375}, {"start": 1697.95, "end": 1698.03, "word": " the", "probability": 0.91552734375}, {"start": 1698.03, "end": 1698.21, "word": " middle", "probability": 0.95263671875}, {"start": 1698.21, "end": 1698.41, "word": " is", "probability": 0.94287109375}, {"start": 1698.41, "end": 1698.67, "word": " 3", "probability": 0.52001953125}, {"start": 1698.67, "end": 1699.99, "word": " because", "probability": 0.5986328125}, {"start": 1699.99, "end": 1701.19, "word": " there", "probability": 0.9111328125}, {"start": 1701.19, "end": 1701.43, "word": " are", "probability": 0.94189453125}, {"start": 1701.43, "end": 1701.63, "word": " two", "probability": 0.8662109375}, {"start": 1701.63, "end": 1702.33, "word": " pillows.", "probability": 0.238525390625}], "temperature": 1.0}, {"id": 63, "seek": 172542, "start": 1704.86, "end": 1725.42, "text": " And also there are the same number of observations above it. So 3 is the median. Now again imagine we replace 5, which is the maximum value, by another one which is extreme one, for example 10. In this case, the median is still 3.", "tokens": [400, 611, 456, 366, 264, 912, 1230, 295, 18163, 3673, 309, 13, 407, 805, 307, 264, 26779, 13, 823, 797, 3811, 321, 7406, 1025, 11, 597, 307, 264, 6674, 2158, 11, 538, 1071, 472, 597, 307, 8084, 472, 11, 337, 1365, 1266, 13, 682, 341, 1389, 11, 264, 26779, 307, 920, 805, 13], "avg_logprob": -0.16984953979651132, "compression_ratio": 1.4085365853658536, "no_speech_prob": 0.0, "words": [{"start": 1704.86, "end": 1705.24, "word": " And", "probability": 0.7255859375}, {"start": 1705.24, "end": 1705.62, "word": " also", "probability": 0.8349609375}, {"start": 1705.62, "end": 1705.82, "word": " there", "probability": 0.65673828125}, {"start": 1705.82, "end": 1705.96, "word": " are", "probability": 0.9306640625}, {"start": 1705.96, "end": 1706.12, "word": " the", "probability": 0.91552734375}, {"start": 1706.12, "end": 1706.34, "word": " same", "probability": 0.89892578125}, {"start": 1706.34, "end": 1706.64, "word": " number", "probability": 0.91796875}, {"start": 1706.64, "end": 1706.8, "word": " of", "probability": 0.947265625}, {"start": 1706.8, "end": 1707.3, "word": " observations", "probability": 0.80224609375}, {"start": 1707.3, "end": 1708.14, "word": " above", "probability": 0.94140625}, {"start": 1708.14, "end": 1708.48, "word": " it.", "probability": 0.95068359375}, {"start": 1708.94, "end": 1709.06, "word": " So", "probability": 0.95361328125}, {"start": 1709.06, "end": 1709.38, "word": " 3", "probability": 0.36962890625}, {"start": 1709.38, "end": 1709.64, "word": " is", "probability": 0.95068359375}, {"start": 1709.64, "end": 1709.82, "word": " the", "probability": 0.92041015625}, {"start": 1709.82, "end": 1710.0, "word": " median.", "probability": 0.93994140625}, {"start": 1711.54, "end": 1711.76, "word": " Now", "probability": 0.95751953125}, {"start": 1711.76, "end": 1711.98, "word": " again", "probability": 0.7978515625}, {"start": 1711.98, "end": 1712.38, "word": " imagine", "probability": 0.63037109375}, {"start": 1712.38, "end": 1713.14, "word": " we", "probability": 0.55126953125}, {"start": 1713.14, "end": 1713.54, "word": " replace", "probability": 0.90625}, {"start": 1713.54, "end": 1714.22, "word": " 5,", "probability": 0.95263671875}, {"start": 1714.36, "end": 1714.54, "word": " which", "probability": 0.94384765625}, {"start": 1714.54, "end": 1714.68, "word": " is", "probability": 0.94775390625}, {"start": 1714.68, "end": 1714.9, "word": " the", "probability": 0.9150390625}, {"start": 1714.9, "end": 1715.52, "word": " maximum", "probability": 0.91259765625}, {"start": 1715.52, "end": 1716.12, "word": " value,", "probability": 0.97265625}, {"start": 1716.42, "end": 1716.86, "word": " by", "probability": 0.94775390625}, {"start": 1716.86, "end": 1717.32, "word": " another", "probability": 0.9208984375}, {"start": 1717.32, "end": 1717.62, "word": " one", "probability": 0.90673828125}, {"start": 1717.62, "end": 1717.76, "word": " which", "probability": 0.5751953125}, {"start": 1717.76, "end": 1717.88, "word": " is", "probability": 0.951171875}, {"start": 1717.88, "end": 1718.36, "word": " extreme", "probability": 0.751953125}, {"start": 1718.36, "end": 1718.62, "word": " one,", "probability": 0.82177734375}, {"start": 1718.68, "end": 1718.82, "word": " for", "probability": 0.95166015625}, {"start": 1718.82, "end": 1719.14, "word": " example", "probability": 0.96875}, {"start": 1719.14, "end": 1719.46, "word": " 10.", "probability": 0.6640625}, {"start": 1721.28, "end": 1721.92, "word": " In", "probability": 0.96435546875}, {"start": 1721.92, "end": 1722.14, "word": " this", "probability": 0.94580078125}, {"start": 1722.14, "end": 1722.54, "word": " case,", "probability": 0.9072265625}, {"start": 1722.92, "end": 1724.14, "word": " the", "probability": 0.90380859375}, {"start": 1724.14, "end": 1724.46, "word": " median", "probability": 0.955078125}, {"start": 1724.46, "end": 1724.82, "word": " is", "probability": 0.9404296875}, {"start": 1724.82, "end": 1725.14, "word": " still", "probability": 0.96337890625}, {"start": 1725.14, "end": 1725.42, "word": " 3.", "probability": 0.7177734375}], "temperature": 1.0}, {"id": 64, "seek": 174954, "start": 1726.4, "end": 1749.54, "text": " Because the median is just the value of the middle after you arrange the data. So it doesn't matter what is the highest or the maximum value is, the median in this case is three. It doesn't change. That means the median is not affected by extreme values. Or to be more precise, we can say that", "tokens": [1436, 264, 26779, 307, 445, 264, 2158, 295, 264, 2808, 934, 291, 9424, 264, 1412, 13, 407, 309, 1177, 380, 1871, 437, 307, 264, 6343, 420, 264, 6674, 2158, 307, 11, 264, 26779, 294, 341, 1389, 307, 1045, 13, 467, 1177, 380, 1319, 13, 663, 1355, 264, 26779, 307, 406, 8028, 538, 8084, 4190, 13, 1610, 281, 312, 544, 13600, 11, 321, 393, 584, 300], "avg_logprob": -0.13529829793807233, "compression_ratio": 1.6153846153846154, "no_speech_prob": 0.0, "words": [{"start": 1726.4, "end": 1726.82, "word": " Because", "probability": 0.56591796875}, {"start": 1726.82, "end": 1727.0, "word": " the", "probability": 0.9169921875}, {"start": 1727.0, "end": 1727.24, "word": " median", "probability": 0.9697265625}, {"start": 1727.24, "end": 1727.6, "word": " is", "probability": 0.94287109375}, {"start": 1727.6, "end": 1727.82, "word": " just", "probability": 0.91259765625}, {"start": 1727.82, "end": 1727.98, "word": " the", "probability": 0.921875}, 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So affect the mean much more than the median. I mean, you cannot say for this example, yes, the median is not affected because the median was three, it becomes three. But in another examples, there is small difference between all.", "tokens": [440, 26779, 307, 8028, 538, 484, 2753, 11, 457, 406, 264, 912, 382, 264, 914, 13, 407, 3345, 264, 914, 709, 544, 813, 264, 26779, 13, 286, 914, 11, 291, 2644, 584, 337, 341, 1365, 11, 2086, 11, 264, 26779, 307, 406, 8028, 570, 264, 26779, 390, 1045, 11, 309, 3643, 1045, 13, 583, 294, 1071, 5110, 11, 456, 307, 1359, 2649, 1296, 439, 13], "avg_logprob": -0.20572917366569693, "compression_ratio": 1.7209302325581395, "no_speech_prob": 0.00018799304962158203, "words": [{"start": 1750.29, "end": 1750.93, "word": " The", "probability": 0.489501953125}, {"start": 1750.93, "end": 1751.21, "word": " median", "probability": 0.96728515625}, {"start": 1751.21, "end": 1751.97, "word": " is", "probability": 0.94482421875}, {"start": 1751.97, "end": 1752.47, "word": " affected", "probability": 0.85986328125}, {"start": 1752.47, "end": 1752.91, "word": " by", "probability": 0.97021484375}, {"start": 1752.91, "end": 1753.37, 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If the dataset has extreme values, we have to use, what do you think, the mean or the median? The median. So in case or in the presence of extreme values or outliers, we have to use the median, not the mean. 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The mean is much better than the median in this case. But if the data has extreme values or outliers, we should use the median instead of the mean.", "tokens": [759, 264, 1412, 307, 1737, 295, 484, 23646, 11, 286, 914, 498, 264, 1412, 575, 406, 8084, 4190, 11, 550, 291, 393, 764, 264, 914, 13, 440, 914, 307, 709, 1101, 813, 264, 26779, 294, 341, 1389, 13, 583, 498, 264, 1412, 575, 8084, 4190, 420, 484, 23646, 11, 321, 820, 764, 264, 26779, 2602, 295, 264, 914, 13], "avg_logprob": -0.10455729104578496, "compression_ratio": 1.767605633802817, "no_speech_prob": 0.0, "words": [{"start": 1806.67, "end": 1807.01, "word": " If", "probability": 0.748046875}, {"start": 1807.01, "end": 1807.21, "word": " the", "probability": 0.904296875}, {"start": 1807.21, "end": 1807.55, "word": " data", "probability": 0.9482421875}, {"start": 1807.55, "end": 1807.91, "word": " is", "probability": 0.91162109375}, {"start": 1807.91, "end": 1808.25, "word": " free", "probability": 0.9267578125}, {"start": 1808.25, "end": 1808.45, "word": " of", "probability": 0.97021484375}, {"start": 1808.45, "end": 1808.97, "word": " outliers,", "probability": 0.943603515625}, {"start": 1809.45, "end": 1809.55, "word": " I", "probability": 0.90234375}, {"start": 1809.55, "end": 1809.73, "word": " mean", "probability": 0.96728515625}, {"start": 1809.73, "end": 1810.27, "word": " if", "probability": 0.5576171875}, {"start": 1810.27, "end": 1810.45, "word": " the", "probability": 0.91650390625}, {"start": 1810.45, "end": 1810.77, "word": " data", "probability": 0.94140625}, {"start": 1810.77, "end": 1812.95, "word": " has", "probability": 0.89892578125}, {"start": 1812.95, "end": 1813.21, "word": " not", "probability": 0.76806640625}, {"start": 1813.21, "end": 1813.57, "word": " extreme", "probability": 0.84423828125}, {"start": 1813.57, "end": 1814.05, "word": " values,", "probability": 0.96875}, {"start": 1814.59, "end": 1814.95, "word": " then", "probability": 0.859375}, {"start": 1814.95, "end": 1815.09, "word": " you", "probability": 0.94775390625}, {"start": 1815.09, "end": 1815.31, "word": " can", "probability": 0.9462890625}, {"start": 1815.31, "end": 1815.77, "word": " use", "probability": 0.873046875}, {"start": 1815.77, "end": 1816.27, "word": " the", "probability": 0.8896484375}, {"start": 1816.27, "end": 1816.41, "word": " mean.", "probability": 0.95751953125}, {"start": 1816.51, "end": 1816.65, "word": " The", "probability": 0.88330078125}, {"start": 1816.65, "end": 1816.75, "word": " mean", "probability": 0.97216796875}, {"start": 1816.75, "end": 1816.89, "word": " is", "probability": 0.95751953125}, {"start": 1816.89, "end": 1817.17, "word": " much", "probability": 0.91748046875}, {"start": 1817.17, "end": 1817.47, "word": " better", "probability": 0.9013671875}, {"start": 1817.47, "end": 1817.83, "word": " than", "probability": 0.94921875}, {"start": 1817.83, "end": 1818.63, "word": " the", "probability": 0.923828125}, {"start": 1818.63, "end": 1818.81, "word": " median", "probability": 0.9404296875}, {"start": 1818.81, "end": 1819.05, "word": " in", "probability": 0.896484375}, {"start": 1819.05, "end": 1819.23, "word": " this", "probability": 0.94873046875}, {"start": 1819.23, "end": 1819.47, "word": " case.", "probability": 0.90771484375}, {"start": 1819.53, "end": 1819.77, "word": " But", "probability": 0.93408203125}, {"start": 1819.77, "end": 1820.07, "word": " if", "probability": 0.87451171875}, {"start": 1820.07, "end": 1820.25, "word": " the", "probability": 0.9169921875}, {"start": 1820.25, "end": 1820.59, "word": " data", "probability": 0.9384765625}, {"start": 1820.59, "end": 1821.59, "word": " has", "probability": 0.94970703125}, {"start": 1821.59, "end": 1822.03, "word": " extreme", "probability": 0.841796875}, {"start": 1822.03, "end": 1822.35, "word": " values", "probability": 0.97265625}, {"start": 1822.35, "end": 1822.49, "word": " or", "probability": 0.90771484375}, {"start": 1822.49, "end": 1822.97, "word": " outliers,", "probability": 0.9560546875}, {"start": 1823.33, "end": 1823.59, "word": " we", "probability": 0.931640625}, {"start": 1823.59, "end": 1823.85, "word": " should", "probability": 0.96533203125}, {"start": 1823.85, "end": 1824.25, "word": " use", "probability": 0.87255859375}, {"start": 1824.25, "end": 1824.67, "word": " the", "probability": 0.92333984375}, {"start": 1824.67, "end": 1824.89, "word": " median", "probability": 0.953125}, {"start": 1824.89, "end": 1826.31, "word": " instead", "probability": 0.8779296875}, {"start": 1826.31, "end": 1826.85, "word": " of", "probability": 0.96826171875}, {"start": 1826.85, "end": 1827.19, "word": " the", "probability": 0.93115234375}, {"start": 1827.19, "end": 1827.31, "word": " mean.", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 68, "seek": 184647, "start": 1827.97, "end": 1846.47, "text": " Any question? So these are the most common center tendency measures in statistics, the mean and the median. And keep in mind, your data should be numeric. I mean, you cannot use the mean or the median", "tokens": [2639, 1168, 30, 407, 613, 366, 264, 881, 2689, 3056, 18187, 8000, 294, 12523, 11, 264, 914, 293, 264, 26779, 13, 400, 1066, 294, 1575, 11, 428, 1412, 820, 312, 7866, 299, 13, 286, 914, 11, 291, 2644, 764, 264, 914, 420, 264, 26779], "avg_logprob": -0.13940972222222223, "compression_ratio": 1.488888888888889, "no_speech_prob": 0.0, "words": [{"start": 1827.97, "end": 1828.25, "word": " Any", "probability": 0.74560546875}, {"start": 1828.25, "end": 1828.55, "word": " question?", "probability": 0.76611328125}, {"start": 1829.19, "end": 1829.77, "word": " So", "probability": 0.92236328125}, {"start": 1829.77, "end": 1830.03, "word": " these", "probability": 0.7001953125}, {"start": 1830.03, "end": 1830.27, "word": " are", "probability": 0.9462890625}, {"start": 1830.27, "end": 1830.45, "word": " the", "probability": 0.9228515625}, {"start": 1830.45, "end": 1830.73, "word": " most", "probability": 0.90673828125}, {"start": 1830.73, "end": 1831.31, "word": " common", "probability": 0.884765625}, {"start": 1831.31, "end": 1833.65, "word": " center", "probability": 0.62109375}, {"start": 1833.65, "end": 1834.05, "word": " tendency", "probability": 0.83447265625}, {"start": 1834.05, "end": 1834.59, "word": " measures", "probability": 0.822265625}, {"start": 1834.59, "end": 1835.11, "word": " in", "probability": 0.93408203125}, {"start": 1835.11, "end": 1835.67, "word": " statistics,", "probability": 0.853515625}, {"start": 1836.33, "end": 1836.47, "word": " the", "probability": 0.9189453125}, {"start": 1836.47, "end": 1836.71, "word": " mean", "probability": 0.96484375}, {"start": 1836.71, "end": 1837.97, "word": " and", "probability": 0.8154296875}, {"start": 1837.97, "end": 1838.15, "word": " the", "probability": 0.91796875}, {"start": 1838.15, "end": 1838.37, "word": " median.", "probability": 0.95166015625}, {"start": 1839.23, "end": 1839.51, "word": " And", "probability": 0.9150390625}, {"start": 1839.51, "end": 1839.67, "word": " keep", "probability": 0.92333984375}, {"start": 1839.67, "end": 1839.79, "word": " in", "probability": 0.947265625}, {"start": 1839.79, "end": 1840.15, "word": " mind,", "probability": 0.88623046875}, {"start": 1841.29, "end": 1841.63, "word": " your", "probability": 0.8955078125}, {"start": 1841.63, "end": 1842.09, "word": " data", "probability": 0.9501953125}, {"start": 1842.09, "end": 1842.39, "word": " should", "probability": 0.96533203125}, {"start": 1842.39, "end": 1842.57, "word": " be", "probability": 0.958984375}, {"start": 1842.57, "end": 1843.17, "word": " numeric.", "probability": 0.90234375}, {"start": 1843.93, "end": 1844.07, "word": " I", "probability": 0.9541015625}, {"start": 1844.07, "end": 1844.23, "word": " mean,", "probability": 0.962890625}, {"start": 1844.53, "end": 1844.77, "word": " you", "probability": 0.9658203125}, {"start": 1844.77, "end": 1845.11, "word": " cannot", "probability": 0.89111328125}, {"start": 1845.11, "end": 1845.53, "word": " use", "probability": 0.8779296875}, {"start": 1845.53, "end": 1845.71, "word": " the", "probability": 0.9267578125}, {"start": 1845.71, "end": 1845.85, "word": " mean", "probability": 0.97509765625}, {"start": 1845.85, "end": 1846.01, "word": " or", "probability": 0.96240234375}, {"start": 1846.01, "end": 1846.17, "word": " the", "probability": 0.92578125}, {"start": 1846.17, "end": 1846.47, "word": " median", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 69, "seek": 186981, "start": 1848.01, "end": 1869.81, "text": " for qualitative or categorical data, for example, gender, males or females. You cannot say the mean of gender or sex is 1.5. It doesn't make sense. It should be numerical data to use the mean or the median. So the mean and the median is used only for numerical data.", "tokens": [337, 31312, 420, 19250, 804, 1412, 11, 337, 1365, 11, 7898, 11, 20776, 420, 21529, 13, 509, 2644, 584, 264, 914, 295, 7898, 420, 3260, 307, 502, 13, 20, 13, 467, 1177, 380, 652, 2020, 13, 467, 820, 312, 29054, 1412, 281, 764, 264, 914, 420, 264, 26779, 13, 407, 264, 914, 293, 264, 26779, 307, 1143, 787, 337, 29054, 1412, 13], "avg_logprob": -0.13541666950498307, "compression_ratio": 1.6583850931677018, "no_speech_prob": 0.0, "words": [{"start": 1848.01, "end": 1848.61, "word": " for", "probability": 0.60693359375}, {"start": 1848.61, "end": 1849.19, "word": " qualitative", "probability": 0.88330078125}, {"start": 1849.19, "end": 1849.61, "word": " or", "probability": 0.91650390625}, {"start": 1849.61, "end": 1850.09, "word": " categorical", "probability": 0.748779296875}, {"start": 1850.09, "end": 1850.51, "word": " data,", "probability": 0.9384765625}, {"start": 1850.63, "end": 1850.73, "word": " for", "probability": 0.94677734375}, {"start": 1850.73, "end": 1851.03, "word": " example,", "probability": 0.97998046875}, {"start": 1851.15, "end": 1851.45, "word": " gender,", "probability": 0.83837890625}, {"start": 1851.59, "end": 1851.75, "word": " males", "probability": 0.947265625}, {"start": 1851.75, "end": 1851.95, "word": " or", "probability": 0.908203125}, {"start": 1851.95, "end": 1852.25, "word": " females.", "probability": 0.9541015625}, {"start": 1852.67, "end": 1852.89, "word": " You", "probability": 0.8291015625}, {"start": 1852.89, "end": 1853.65, "word": " cannot", "probability": 0.841796875}, {"start": 1853.65, "end": 1854.31, "word": " say", "probability": 0.9501953125}, {"start": 1854.31, "end": 1855.19, "word": " the", "probability": 0.80810546875}, {"start": 1855.19, "end": 1855.55, "word": " mean", "probability": 0.97265625}, {"start": 1855.55, "end": 1856.51, "word": " of", "probability": 0.970703125}, {"start": 1856.51, "end": 1856.99, "word": " gender", "probability": 0.87744140625}, {"start": 1856.99, "end": 1857.21, "word": " or", "probability": 0.95703125}, {"start": 1857.21, "end": 1857.51, "word": " sex", "probability": 0.95166015625}, {"start": 1857.51, "end": 1857.73, "word": " is", "probability": 0.94140625}, {"start": 1857.73, "end": 1857.97, "word": " 1", "probability": 0.978515625}, {"start": 1857.97, "end": 1858.51, "word": ".5.", "probability": 0.998779296875}, {"start": 1858.83, "end": 1858.99, "word": " It", "probability": 0.9560546875}, {"start": 1858.99, "end": 1859.27, "word": " doesn't", "probability": 0.967529296875}, {"start": 1859.27, "end": 1859.49, "word": " make", "probability": 0.93603515625}, {"start": 1859.49, "end": 1859.81, "word": " sense.", "probability": 0.8330078125}, {"start": 1861.29, "end": 1861.65, "word": " It", "probability": 0.96875}, {"start": 1861.65, "end": 1861.85, "word": " should", "probability": 0.9658203125}, {"start": 1861.85, "end": 1862.01, "word": " be", "probability": 0.95751953125}, {"start": 1862.01, "end": 1862.37, "word": " numerical", "probability": 0.91796875}, {"start": 1862.37, "end": 1862.87, "word": " data", "probability": 0.939453125}, {"start": 1862.87, "end": 1863.83, "word": " to", "probability": 0.95556640625}, {"start": 1863.83, "end": 1864.27, "word": " use", "probability": 0.87060546875}, {"start": 1864.27, "end": 1865.29, "word": " the", "probability": 0.9169921875}, {"start": 1865.29, "end": 1865.49, "word": " mean", "probability": 0.97998046875}, {"start": 1865.49, "end": 1865.67, "word": " or", "probability": 0.95849609375}, {"start": 1865.67, "end": 1865.81, "word": " the", "probability": 0.9228515625}, {"start": 1865.81, "end": 1865.99, "word": " median.", "probability": 0.91015625}, {"start": 1866.11, "end": 1866.21, "word": " So", "probability": 0.9248046875}, {"start": 1866.21, "end": 1866.35, "word": " the", "probability": 0.72998046875}, {"start": 1866.35, "end": 1866.49, "word": " mean", "probability": 0.970703125}, {"start": 1866.49, "end": 1866.63, "word": " and", "probability": 0.6748046875}, {"start": 1866.63, "end": 1866.77, "word": " the", "probability": 0.8740234375}, {"start": 1866.77, "end": 1866.97, "word": " median", "probability": 0.9599609375}, {"start": 1866.97, "end": 1867.25, "word": " is", "probability": 0.9267578125}, {"start": 1867.25, "end": 1867.59, "word": " used", "probability": 0.91650390625}, {"start": 1867.59, "end": 1868.01, "word": " only", "probability": 0.93212890625}, {"start": 1868.01, "end": 1868.47, "word": " for", "probability": 0.95263671875}, {"start": 1868.47, "end": 1869.27, "word": " numerical", "probability": 0.70556640625}, {"start": 1869.27, "end": 1869.81, "word": " data.", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 70, "seek": 189759, "start": 1870.51, "end": 1897.59, "text": " And we have to distinguish between mean and median. Mean is used for data that has not outliers or extreme values, while the median is used for data that has outliers or extreme values. Sometimes better to report both. I mean, sometimes better to report mean and the median. So you just say the sales for this company is, for example, $500,000.", "tokens": [400, 321, 362, 281, 20206, 1296, 914, 293, 26779, 13, 12302, 307, 1143, 337, 1412, 300, 575, 406, 484, 23646, 420, 8084, 4190, 11, 1339, 264, 26779, 307, 1143, 337, 1412, 300, 575, 484, 23646, 420, 8084, 4190, 13, 4803, 1101, 281, 2275, 1293, 13, 286, 914, 11, 2171, 1101, 281, 2275, 914, 293, 264, 26779, 13, 407, 291, 445, 584, 264, 5763, 337, 341, 2237, 307, 11, 337, 1365, 11, 1848, 7526, 11, 1360, 13], "avg_logprob": -0.13900162260253707, "compression_ratio": 1.806282722513089, "no_speech_prob": 0.0, "words": [{"start": 1870.51, "end": 1870.83, "word": " And", "probability": 0.494873046875}, {"start": 1870.83, "end": 1870.95, "word": " we", "probability": 0.779296875}, {"start": 1870.95, "end": 1871.09, "word": " have", "probability": 0.9267578125}, {"start": 1871.09, "end": 1871.21, "word": " to", "probability": 0.958984375}, {"start": 1871.21, "end": 1871.63, "word": " distinguish", "probability": 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You can see that. Is it clear? If you have a small data, it's straightforward and it's very easy to locate the median. But in case of large dataset, how can we locate the median? It's not easy. Just look at the data and", "tokens": [400, 264, 26779, 11, 337, 1365, 11, 307, 42514, 11, 1360, 13, 509, 393, 536, 300, 13, 1119, 309, 1850, 30, 759, 291, 362, 257, 1359, 1412, 11, 309, 311, 15325, 293, 309, 311, 588, 1858, 281, 22370, 264, 26779, 13, 583, 294, 1389, 295, 2416, 28872, 11, 577, 393, 321, 22370, 264, 26779, 30, 467, 311, 406, 1858, 13, 1449, 574, 412, 264, 1412, 293], "avg_logprob": -0.126515858653766, "compression_ratio": 1.5174418604651163, "no_speech_prob": 0.0, "words": [{"start": 1900.06, "end": 1900.38, "word": " And", "probability": 0.74609375}, {"start": 1900.38, "end": 1900.56, "word": " the", "probability": 0.912109375}, {"start": 1900.56, "end": 1900.88, "word": " median,", "probability": 0.95361328125}, {"start": 1901.12, "end": 1901.22, "word": " for", "probability": 0.951171875}, {"start": 1901.22, "end": 1901.58, "word": " example,", "probability": 0.9765625}, {"start": 1901.7, "end": 1901.8, "word": " is", "probability": 0.9130859375}, {"start": 1901.8, "end": 1902.38, "word": " 550", "probability": 0.90185546875}, {"start": 1902.38, "end": 1902.82, "word": ",000.", "probability": 0.885498046875}, {"start": 1903.08, "end": 1903.3, "word": " You", "probability": 0.95703125}, {"start": 1903.3, "end": 1903.52, "word": " can", "probability": 0.947265625}, {"start": 1903.52, "end": 1903.7, "word": " see", "probability": 0.8056640625}, {"start": 1903.7, "end": 1903.9, "word": " that.", "probability": 0.88720703125}, {"start": 1905.68, "end": 1905.98, "word": " Is", "probability": 0.92041015625}, {"start": 1905.98, "end": 1906.1, "word": " it", "probability": 0.88720703125}, {"start": 1906.1, "end": 1906.4, "word": " clear?", "probability": 0.9013671875}, {"start": 1911.44, "end": 1911.96, "word": " If", "probability": 0.80419921875}, {"start": 1911.96, "end": 1912.74, "word": " you", "probability": 0.93603515625}, {"start": 1912.74, "end": 1912.88, "word": " have", "probability": 0.95263671875}, {"start": 1912.88, "end": 1912.98, "word": " a", "probability": 0.61962890625}, {"start": 1912.98, "end": 1913.22, "word": " small", "probability": 0.93994140625}, {"start": 1913.22, "end": 1913.58, "word": " data,", "probability": 0.935546875}, {"start": 1914.06, "end": 1914.38, "word": " it's", "probability": 0.961181640625}, {"start": 1914.38, "end": 1915.04, "word": " straightforward", "probability": 0.85595703125}, {"start": 1915.04, "end": 1915.56, "word": " and", "probability": 0.52490234375}, {"start": 1915.56, "end": 1915.8, "word": " it's", "probability": 0.95263671875}, {"start": 1915.8, "end": 1916.02, "word": " very", "probability": 0.85546875}, {"start": 1916.02, "end": 1916.34, "word": " easy", "probability": 0.8994140625}, {"start": 1916.34, "end": 1916.54, "word": " to", "probability": 0.970703125}, {"start": 1916.54, "end": 1916.92, "word": " locate", "probability": 0.94482421875}, {"start": 1916.92, "end": 1917.14, "word": " the", "probability": 0.91455078125}, {"start": 1917.14, "end": 1917.4, "word": " median.", "probability": 0.892578125}, {"start": 1918.44, "end": 1918.72, "word": " But", "probability": 0.9521484375}, {"start": 1918.72, "end": 1918.9, "word": " in", "probability": 0.923828125}, {"start": 1918.9, "end": 1919.18, "word": " case", "probability": 0.87255859375}, {"start": 1919.18, "end": 1919.34, "word": " of", "probability": 0.96728515625}, {"start": 1919.34, "end": 1919.68, "word": " large", "probability": 0.89892578125}, {"start": 1919.68, "end": 1920.14, "word": " dataset,", "probability": 0.45849609375}, {"start": 1920.72, "end": 1920.96, "word": " how", "probability": 0.93408203125}, {"start": 1920.96, "end": 1921.22, "word": " can", "probability": 0.94091796875}, {"start": 1921.22, "end": 1921.38, "word": " we", "probability": 0.748046875}, {"start": 1921.38, "end": 1921.68, "word": " locate", "probability": 0.8310546875}, {"start": 1921.68, "end": 1921.88, "word": " the", "probability": 0.919921875}, {"start": 1921.88, "end": 1922.12, "word": " median?", "probability": 0.9462890625}, {"start": 1922.34, "end": 1922.52, "word": " It's", "probability": 0.959228515625}, {"start": 1922.52, "end": 1922.7, "word": " not", "probability": 0.943359375}, {"start": 1922.7, "end": 1922.98, "word": " easy.", "probability": 0.91064453125}, {"start": 1923.34, "end": 1923.6, "word": " Just", "probability": 0.87158203125}, {"start": 1923.6, "end": 1923.82, "word": " look", "probability": 0.81005859375}, {"start": 1923.82, "end": 1923.94, "word": " at", "probability": 0.96630859375}, {"start": 1923.94, "end": 1924.06, "word": " the", "probability": 0.91552734375}, {"start": 1924.06, "end": 1924.36, "word": " data", "probability": 0.93212890625}, {"start": 1924.36, "end": 1925.16, "word": " and", "probability": 0.79248046875}], "temperature": 1.0}, {"id": 72, "seek": 195120, "start": 1926.2, "end": 1951.2, "text": " you can say this is the median. It's not easy task. So we need a rule that locate the median. The location of the median when the values are in numerical order from smallest to largest is N plus one divided by two. That's the position of the median. If we go back a little bit to the previous example, here N was five.", "tokens": [291, 393, 584, 341, 307, 264, 26779, 13, 467, 311, 406, 1858, 5633, 13, 407, 321, 643, 257, 4978, 300, 22370, 264, 26779, 13, 440, 4914, 295, 264, 26779, 562, 264, 4190, 366, 294, 29054, 1668, 490, 16998, 281, 6443, 307, 426, 1804, 472, 6666, 538, 732, 13, 663, 311, 264, 2535, 295, 264, 26779, 13, 759, 321, 352, 646, 257, 707, 857, 281, 264, 3894, 1365, 11, 510, 426, 390, 1732, 13], "avg_logprob": -0.13239019746715958, "compression_ratio": 1.5870646766169154, "no_speech_prob": 0.0, "words": [{"start": 1926.2, "end": 1926.44, "word": " you", "probability": 0.454833984375}, {"start": 1926.44, "end": 1926.64, "word": " can", "probability": 0.94140625}, {"start": 1926.64, "end": 1926.84, "word": " say", "probability": 0.79443359375}, {"start": 1926.84, "end": 1927.64, "word": " this", "probability": 0.609375}, {"start": 1927.64, "end": 1927.8, "word": " is", "probability": 0.94775390625}, {"start": 1927.8, 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So location number three is the median. Location number one is one, in this case, then two, then three. So location number three is three. But maybe this number is not three, and other value maybe 3.1 or 3.2. But the location is number three. Is it clear?", "tokens": [407, 264, 4914, 390, 1230, 1045, 11, 570, 297, 1804, 472, 6666, 538, 732, 11, 1732, 1804, 472, 6666, 538, 732, 307, 1045, 13, 407, 4914, 1230, 1045, 307, 264, 26779, 13, 12859, 399, 1230, 472, 307, 472, 11, 294, 341, 1389, 11, 550, 732, 11, 550, 1045, 13, 407, 4914, 1230, 1045, 307, 1045, 13, 583, 1310, 341, 1230, 307, 406, 1045, 11, 293, 661, 2158, 1310, 805, 13, 16, 420, 805, 13, 17, 13, 583, 264, 4914, 307, 1230, 1045, 13, 1119, 309, 1850, 30], "avg_logprob": -0.19335937652398238, "compression_ratio": 2.0335195530726256, "no_speech_prob": 0.0, "words": [{"start": 1953.48, "end": 1953.9, "word": " So", "probability": 0.85986328125}, {"start": 1953.9, "end": 1954.28, "word": " the", "probability": 0.70751953125}, {"start": 1954.28, "end": 1954.62, "word": " location", "probability": 0.947265625}, {"start": 1954.62, "end": 1954.98, "word": " was", "probability": 0.95458984375}, {"start": 1954.98, "end": 1955.68, "word": " number", "probability": 0.9345703125}, 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"word": " and", "probability": 0.252685546875}, {"start": 1974.92, "end": 1975.4, "word": " other", "probability": 0.53173828125}, {"start": 1975.4, "end": 1975.64, "word": " value", "probability": 0.66650390625}, {"start": 1975.64, "end": 1975.92, "word": " maybe", "probability": 0.270751953125}, {"start": 1975.92, "end": 1976.62, "word": " 3", "probability": 0.40625}, {"start": 1976.62, "end": 1977.14, "word": ".1", "probability": 0.989501953125}, {"start": 1977.14, "end": 1977.28, "word": " or", "probability": 0.84375}, {"start": 1977.28, "end": 1977.74, "word": " 3", "probability": 0.99072265625}, {"start": 1977.74, "end": 1978.28, "word": ".2.", "probability": 0.995361328125}, {"start": 1978.74, "end": 1978.96, "word": " But", "probability": 0.95556640625}, {"start": 1978.96, "end": 1979.12, "word": " the", "probability": 0.91943359375}, {"start": 1979.12, "end": 1979.52, "word": " location", "probability": 0.935546875}, {"start": 1979.52, "end": 1979.72, "word": " is", 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If it is odd, you mean by odd number, five, seven and so on. So if the number of values is odd, the median is the middle number. Now let's imagine if we have even number of observations. For example, we have one, two, three, four, five and six. So imagine numbers from one up to six. 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three. And three above it. And four is not the median because three observations below, two above. So three and four is the middle value. So just take the average of two middle points,", "tokens": [823, 1045, 307, 406, 264, 26779, 570, 456, 366, 732, 18163, 2507, 1045, 13, 400, 1045, 3673, 309, 13, 400, 1451, 307, 406, 264, 26779, 570, 1045, 18163, 2507, 11, 732, 3673, 13, 407, 1045, 293, 1451, 307, 264, 2808, 2158, 13, 407, 445, 747, 264, 4274, 295, 732, 2808, 2793, 11], "avg_logprob": -0.16597877808336942, "compression_ratio": 1.8142857142857143, "no_speech_prob": 0.0, "words": [{"start": 2011.67, "end": 2012.01, "word": " Now", "probability": 0.90576171875}, {"start": 2012.01, "end": 2012.39, "word": " three", "probability": 0.3642578125}, {"start": 2012.39, "end": 2013.31, "word": " is", "probability": 0.93359375}, {"start": 2013.31, "end": 2013.51, "word": " not", "probability": 0.95361328125}, {"start": 2013.51, "end": 2013.69, "word": " the", "probability": 0.90966796875}, {"start": 2013.69, "end": 2013.95, "word": " median", "probability": 0.958984375}, {"start": 2013.95, "end": 2014.91, "word": " because", "probability": 0.6728515625}, {"start": 2014.91, "end": 2015.19, "word": " there", "probability": 0.9091796875}, {"start": 2015.19, "end": 2015.37, "word": " are", "probability": 0.9423828125}, {"start": 2015.37, "end": 2015.61, "word": " two", "probability": 0.939453125}, {"start": 2015.61, "end": 2016.19, "word": " observations", "probability": 0.75634765625}, {"start": 2016.19, "end": 2016.65, "word": " below", "probability": 0.892578125}, {"start": 2016.65, "end": 2017.63, "word": " three.", "probability": 0.416259765625}, {"start": 2018.91, "end": 2019.59, "word": " And", "probability": 0.6796875}, {"start": 2019.59, "end": 2021.95, "word": " three", "probability": 0.6943359375}, {"start": 2021.95, "end": 2022.39, "word": " above", "probability": 0.94873046875}, {"start": 2022.39, "end": 2022.71, "word": " it.", "probability": 0.951171875}, {"start": 2023.21, "end": 2023.39, "word": " And", "probability": 0.9248046875}, {"start": 2023.39, "end": 2023.61, "word": " four", "probability": 0.935546875}, {"start": 2023.61, "end": 2023.77, "word": " is", "probability": 0.94384765625}, {"start": 2023.77, "end": 2023.95, "word": " not", "probability": 0.9482421875}, {"start": 2023.95, "end": 2024.11, "word": " the", "probability": 0.9267578125}, {"start": 2024.11, "end": 2024.27, "word": " median", "probability": 0.87841796875}, {"start": 2024.27, "end": 2024.75, "word": " because", "probability": 0.86572265625}, {"start": 2024.75, "end": 2025.71, "word": " three", "probability": 0.8876953125}, {"start": 2025.71, "end": 2026.21, "word": " observations", "probability": 0.755859375}, {"start": 2026.21, "end": 2026.73, "word": " below,", "probability": 0.916015625}, {"start": 2027.27, "end": 2027.51, "word": " two", "probability": 0.931640625}, {"start": 2027.51, "end": 2027.87, "word": " above.", "probability": 0.96533203125}, {"start": 2028.61, "end": 2029.29, "word": " So", "probability": 0.96240234375}, {"start": 2029.29, "end": 2029.57, "word": " three", "probability": 0.81689453125}, {"start": 2029.57, "end": 2029.81, "word": " and", "probability": 0.9423828125}, {"start": 2029.81, "end": 2030.29, "word": " four", "probability": 0.94287109375}, {"start": 2030.29, "end": 2032.85, "word": " is", "probability": 0.923828125}, {"start": 2032.85, "end": 2033.07, "word": " the", "probability": 0.91943359375}, {"start": 2033.07, "end": 2033.29, "word": " middle", "probability": 0.94921875}, {"start": 2033.29, "end": 2033.67, "word": " value.", "probability": 0.97998046875}, {"start": 2034.85, "end": 2035.09, "word": " So", "probability": 0.94384765625}, {"start": 2035.09, "end": 2035.39, "word": " just", "probability": 0.82666015625}, {"start": 2035.39, "end": 2035.61, "word": " take", "probability": 0.86572265625}, {"start": 2035.61, "end": 2035.79, "word": " the", "probability": 0.91796875}, {"start": 2035.79, "end": 2036.13, "word": " average", "probability": 0.8232421875}, {"start": 2036.13, "end": 2036.31, "word": " of", "probability": 0.962890625}, {"start": 2036.31, "end": 2036.63, "word": " two", "probability": 0.9013671875}, {"start": 2036.63, "end": 2036.87, "word": " middle", "probability": 0.89501953125}, {"start": 2036.87, "end": 2037.39, "word": " points,", "probability": 0.91259765625}], "temperature": 1.0}, {"id": 76, "seek": 206661, "start": 2038.23, "end": 2066.61, "text": " And that will be the median. So if n is even, you have to locate two middle points. For example, n over 2, in this case, we have six observations. So divide by 2, not n plus 1 divided by 2, just n over 2. So n over 2 is 3. So place number 3, and the next one, place number 4, these are the two middle points. 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The definition of the mood, the mood is the most frequent value. So sometimes the mood exists, sometimes the mood does not exist. Or sometimes there is only one mood, in other cases maybe there are several moods.", "tokens": [5264, 3481, 295, 3056, 18187, 307, 1219, 264, 9268, 13, 440, 7123, 295, 264, 9268, 11, 264, 9268, 307, 264, 881, 18004, 2158, 13, 407, 2171, 264, 9268, 8198, 11, 2171, 264, 9268, 775, 406, 2514, 13, 1610, 2171, 456, 307, 787, 472, 9268, 11, 294, 661, 3331, 1310, 456, 366, 2940, 9268, 82, 13], "avg_logprob": -0.14718191831239633, "compression_ratio": 1.6987179487179487, "no_speech_prob": 0.0, "words": [{"start": 2128.39, "end": 2128.85, "word": " Last", "probability": 0.69091796875}, {"start": 2128.85, "end": 2129.23, "word": " measure", "probability": 0.80712890625}, {"start": 2129.23, "end": 2129.67, "word": " of", "probability": 0.966796875}, {"start": 2129.67, "end": 2129.95, "word": " center", "probability": 0.35009765625}, {"start": 2129.95, "end": 2130.47, "word": " tendency", "probability": 0.91455078125}, {"start": 2130.47, "end": 2130.91, "word": " is", "probability": 0.94189453125}, {"start": 2130.91, "end": 2131.47, "word": " called", "probability": 0.89306640625}, {"start": 2131.47, "end": 2132.51, "word": " the", "probability": 0.6884765625}, {"start": 2132.51, "end": 2132.75, "word": " mood.", "probability": 0.80810546875}, {"start": 2135.89, "end": 2136.65, "word": " The", "probability": 0.86279296875}, {"start": 2136.65, "end": 2137.01, "word": " definition", "probability": 0.94873046875}, {"start": 2137.01, "end": 2137.19, "word": " of", "probability": 0.96826171875}, {"start": 2137.19, "end": 2137.31, "word": " the", "probability": 0.85205078125}, {"start": 2137.31, "end": 2137.49, "word": " mood,", "probability": 0.98046875}, {"start": 2137.57, "end": 2137.69, "word": " the", "probability": 0.86083984375}, {"start": 2137.69, "end": 2137.97, "word": " mood", "probability": 0.97802734375}, {"start": 2137.97, "end": 2138.33, "word": " is", "probability": 0.947265625}, {"start": 2138.33, "end": 2138.59, "word": " the", "probability": 0.91015625}, {"start": 2138.59, "end": 2139.01, "word": " most", "probability": 0.90771484375}, {"start": 2139.01, "end": 2139.65, "word": " frequent", "probability": 0.91796875}, {"start": 2139.65, "end": 2140.29, "word": " value.", "probability": 0.97802734375}, {"start": 2142.29, "end": 2142.45, "word": " So", "probability": 0.546875}, {"start": 2142.45, "end": 2143.05, "word": " sometimes", "probability": 0.79248046875}, {"start": 2143.05, "end": 2143.49, "word": " the", "probability": 0.8671875}, {"start": 2143.49, "end": 2143.67, "word": " mood", "probability": 0.98193359375}, {"start": 2143.67, "end": 2144.25, "word": " exists,", "probability": 0.884765625}, {"start": 2145.23, "end": 2145.57, "word": " sometimes", "probability": 0.94482421875}, {"start": 2145.57, "end": 2145.97, "word": " the", "probability": 0.9140625}, {"start": 2145.97, "end": 2146.09, "word": " mood", "probability": 0.97998046875}, {"start": 2146.09, "end": 2146.29, "word": " does", "probability": 0.97802734375}, {"start": 2146.29, "end": 2146.47, "word": " not", "probability": 0.94921875}, {"start": 2146.47, "end": 2146.91, "word": " exist.", "probability": 0.9697265625}, {"start": 2147.89, "end": 2148.13, "word": " Or", "probability": 0.93017578125}, {"start": 2148.13, "end": 2148.57, "word": " sometimes", "probability": 0.947265625}, {"start": 2148.57, "end": 2148.85, "word": " there", "probability": 0.89501953125}, {"start": 2148.85, "end": 2149.03, "word": " is", "probability": 0.9423828125}, {"start": 2149.03, "end": 2149.35, "word": " only", "probability": 0.92919921875}, {"start": 2149.35, "end": 2149.61, "word": " one", "probability": 0.9228515625}, {"start": 2149.61, "end": 2149.99, "word": " mood,", "probability": 0.986328125}, {"start": 2151.83, "end": 2152.25, "word": " in", "probability": 0.7939453125}, {"start": 2152.25, "end": 2152.53, "word": " other", "probability": 0.892578125}, {"start": 2152.53, "end": 2153.05, "word": " cases", "probability": 0.91650390625}, {"start": 2153.05, "end": 2153.41, "word": " maybe", "probability": 0.7666015625}, {"start": 2153.41, "end": 2153.73, "word": " there", "probability": 0.904296875}, {"start": 2153.73, "end": 2154.11, "word": " are", "probability": 0.943359375}, {"start": 2154.11, "end": 2154.69, "word": " several", "probability": 0.92529296875}, {"start": 2154.69, "end": 2155.35, "word": " moods.", "probability": 0.965576171875}], "temperature": 1.0}, {"id": 80, "seek": 218367, "start": 2156.49, "end": 2183.67, "text": " So a value that occurs most often is called the mood. The mood is not affected by extreme values. It can be used for either numerical or categorical data. And that's the difference between mean and median and the mood. Mean and median is used just for numerical data. Here, the mood can be used for both, categorical and numerical data.", "tokens": [407, 257, 2158, 300, 11843, 881, 2049, 307, 1219, 264, 9268, 13, 440, 9268, 307, 406, 8028, 538, 8084, 4190, 13, 467, 393, 312, 1143, 337, 2139, 29054, 420, 19250, 804, 1412, 13, 400, 300, 311, 264, 2649, 1296, 914, 293, 26779, 293, 264, 9268, 13, 12302, 293, 26779, 307, 1143, 445, 337, 29054, 1412, 13, 1692, 11, 264, 9268, 393, 312, 1143, 337, 1293, 11, 19250, 804, 293, 29054, 1412, 13], "avg_logprob": -0.13184931180248521, "compression_ratio": 1.8216216216216217, "no_speech_prob": 0.0, "words": [{"start": 2156.49, "end": 2156.93, "word": " So", "probability": 0.88134765625}, {"start": 2156.93, "end": 2157.41, "word": " a", "probability": 0.43994140625}, {"start": 2157.41, "end": 2157.73, "word": " value", "probability": 0.9755859375}, {"start": 2157.73, "end": 2157.99, "word": " that", "probability": 0.93896484375}, {"start": 2157.99, "end": 2158.39, "word": " occurs", "probability": 0.77099609375}, 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{"start": 2170.73, "end": 2170.89, "word": " And", "probability": 0.6162109375}, {"start": 2170.89, "end": 2171.07, "word": " that's", "probability": 0.954833984375}, {"start": 2171.07, "end": 2171.19, "word": " the", "probability": 0.916015625}, {"start": 2171.19, "end": 2171.53, "word": " difference", "probability": 0.86083984375}, {"start": 2171.53, "end": 2171.85, "word": " between", "probability": 0.8876953125}, {"start": 2171.85, "end": 2172.01, "word": " mean", "probability": 0.92333984375}, {"start": 2172.01, "end": 2172.19, "word": " and", "probability": 0.9453125}, {"start": 2172.19, "end": 2172.51, "word": " median", "probability": 0.68603515625}, {"start": 2172.51, "end": 2173.57, "word": " and", "probability": 0.65576171875}, {"start": 2173.57, "end": 2173.71, "word": " the", "probability": 0.8955078125}, {"start": 2173.71, "end": 2173.91, "word": " mood.", "probability": 0.9443359375}, {"start": 2174.59, "end": 2174.73, "word": " Mean", "probability": 0.9326171875}, {"start": 2174.73, "end": 2174.91, "word": " and", "probability": 0.94384765625}, {"start": 2174.91, "end": 2175.09, "word": " median", "probability": 0.95068359375}, {"start": 2175.09, "end": 2175.35, "word": " is", "probability": 0.93505859375}, {"start": 2175.35, "end": 2175.55, "word": " used", "probability": 0.91455078125}, {"start": 2175.55, "end": 2175.81, "word": " just", "probability": 0.91748046875}, {"start": 2175.81, "end": 2175.99, "word": " for", "probability": 0.95263671875}, {"start": 2175.99, "end": 2176.39, "word": " numerical", "probability": 0.9130859375}, {"start": 2176.39, "end": 2176.93, "word": " data.", "probability": 0.93310546875}, {"start": 2177.43, "end": 2177.65, "word": " Here,", "probability": 0.8583984375}, {"start": 2177.81, "end": 2177.95, "word": " the", "probability": 0.92529296875}, {"start": 2177.95, "end": 2178.13, "word": " mood", "probability": 0.986328125}, {"start": 2178.13, "end": 2178.49, "word": " can", "probability": 0.94189453125}, {"start": 2178.49, "end": 2178.69, "word": " be", "probability": 0.95703125}, {"start": 2178.69, "end": 2178.95, "word": " used", "probability": 0.91064453125}, {"start": 2178.95, "end": 2179.19, "word": " for", "probability": 0.94775390625}, {"start": 2179.19, "end": 2179.59, "word": " both,", "probability": 0.88623046875}, {"start": 2180.71, "end": 2181.27, "word": " categorical", "probability": 0.9248046875}, {"start": 2181.27, "end": 2181.85, "word": " and", "probability": 0.94140625}, {"start": 2181.85, "end": 2182.97, "word": " numerical", "probability": 0.91162109375}, {"start": 2182.97, "end": 2183.67, "word": " data.", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 81, "seek": 220921, "start": 2184.33, "end": 2209.21, "text": " Sometimes, as I mentioned, there may be no mood or the mood does not exist. In other cases, there may be several events. So the mood is the value that has the most frequent. For example, if you look at this data, one is repeated once, three is the same one time, five is repeated twice.", "tokens": [4803, 11, 382, 286, 2835, 11, 456, 815, 312, 572, 9268, 420, 264, 9268, 775, 406, 2514, 13, 682, 661, 3331, 11, 456, 815, 312, 2940, 3931, 13, 407, 264, 9268, 307, 264, 2158, 300, 575, 264, 881, 18004, 13, 1171, 1365, 11, 498, 291, 574, 412, 341, 1412, 11, 472, 307, 10477, 1564, 11, 1045, 307, 264, 912, 472, 565, 11, 1732, 307, 10477, 6091, 13], "avg_logprob": -0.15211397212217836, "compression_ratio": 1.64, "no_speech_prob": 0.0, "words": [{"start": 2184.33, "end": 2184.89, "word": " Sometimes,", "probability": 0.80029296875}, {"start": 2185.03, "end": 2185.13, "word": " as", "probability": 0.9599609375}, {"start": 2185.13, "end": 2185.25, "word": " I", "probability": 0.9833984375}, {"start": 2185.25, "end": 2185.61, "word": " mentioned,", "probability": 0.80615234375}, {"start": 2185.93, "end": 2186.27, "word": " there", "probability": 0.90869140625}, 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that", "probability": 0.9287109375}, {"start": 2195.55, "end": 2195.93, "word": " has", "probability": 0.7822265625}, {"start": 2195.93, "end": 2196.11, "word": " the", "probability": 0.90234375}, {"start": 2196.11, "end": 2196.41, "word": " most", "probability": 0.9033203125}, {"start": 2196.41, "end": 2196.87, "word": " frequent.", "probability": 0.740234375}, {"start": 2197.49, "end": 2197.75, "word": " For", "probability": 0.95751953125}, {"start": 2197.75, "end": 2198.11, "word": " example,", "probability": 0.97265625}, {"start": 2198.55, "end": 2198.73, "word": " if", "probability": 0.94775390625}, {"start": 2198.73, "end": 2198.79, "word": " you", "probability": 0.9521484375}, {"start": 2198.79, "end": 2198.93, "word": " look", "probability": 0.96484375}, {"start": 2198.93, "end": 2199.05, "word": " at", "probability": 0.96630859375}, {"start": 2199.05, "end": 2199.25, "word": " this", "probability": 0.943359375}, {"start": 2199.25, "end": 2199.61, "word": " data,", 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0.92724609375}, {"start": 2208.37, "end": 2208.69, "word": " repeated", "probability": 0.95556640625}, {"start": 2208.69, "end": 2209.21, "word": " twice.", "probability": 0.95361328125}], "temperature": 1.0}, {"id": 82, "seek": 223601, "start": 2210.39, "end": 2236.01, "text": " seven is one nine is repeated three times and so on so in this case nine is the mood because the mood again is the most frequent value on the right side there are some values zero one two three up to six now each one is repeated once so in this case the mood does not exist I mean there is no mood", "tokens": [3407, 307, 472, 4949, 307, 10477, 1045, 1413, 293, 370, 322, 370, 294, 341, 1389, 4949, 307, 264, 9268, 570, 264, 9268, 797, 307, 264, 881, 18004, 2158, 322, 264, 558, 1252, 456, 366, 512, 4190, 4018, 472, 732, 1045, 493, 281, 2309, 586, 1184, 472, 307, 10477, 1564, 370, 294, 341, 1389, 264, 9268, 775, 406, 2514, 286, 914, 456, 307, 572, 9268], "avg_logprob": -0.16298076923076923, "compression_ratio": 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It can be used for numerical or categorical data, not affected by extreme values or outliers. Sometimes there is only one mood as this example. Sometimes the mood does not exist. Or sometimes there are several moods. And so that's the definitions for mean, median, and the mood.", "tokens": [407, 5101, 4124, 11, 264, 9268, 307, 264, 2158, 300, 291, 1127, 881, 2049, 13, 467, 393, 312, 1143, 337, 29054, 420, 19250, 804, 1412, 11, 406, 8028, 538, 8084, 4190, 420, 484, 23646, 13, 4803, 456, 307, 787, 472, 9268, 382, 341, 1365, 13, 4803, 264, 9268, 775, 406, 2514, 13, 1610, 2171, 456, 366, 2940, 9268, 82, 13, 400, 370, 300, 311, 264, 21988, 337, 914, 11, 26779, 11, 293, 264, 9268, 13], "avg_logprob": -0.14360608827126653, "compression_ratio": 1.674641148325359, "no_speech_prob": 0.0, "words": [{"start": 2238.45, "end": 2238.93, "word": " So", "probability": 0.88330078125}, {"start": 2238.93, "end": 2239.47, "word": " generally", "probability": 0.62548828125}, {"start": 2239.47, "end": 2239.99, "word": " speaking,", "probability": 0.87158203125}, {"start": 2240.31, "end": 2240.41, "word": " the", "probability": 0.916015625}, {"start": 2240.41, "end": 2240.65, "word": " mood", "probability": 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{"start": 2263.83, "end": 2263.97, "word": " the", "probability": 0.921875}, {"start": 2263.97, "end": 2264.39, "word": " definitions", "probability": 0.75146484375}, {"start": 2264.39, "end": 2264.81, "word": " for", "probability": 0.9443359375}, {"start": 2264.81, "end": 2265.19, "word": " mean,", "probability": 0.89453125}, {"start": 2266.43, "end": 2266.75, "word": " median,", "probability": 0.95166015625}, {"start": 2267.67, "end": 2267.97, "word": " and", "probability": 0.9521484375}, {"start": 2267.97, "end": 2268.07, "word": " the", "probability": 0.8759765625}, {"start": 2268.07, "end": 2268.25, "word": " mood.", "probability": 0.91162109375}], "temperature": 1.0}, {"id": 84, "seek": 229992, "start": 2271.0, "end": 2299.92, "text": " I will give just a numerical example to know how can we compute these measures. This data, simple data, just for illustration, we have house prices. We have five data points, $2 million. This is the price of house A, for example. House B price is 500,000. The other one is 300,000. And two houses have the same price as 100,000.", "tokens": [286, 486, 976, 445, 257, 29054, 1365, 281, 458, 577, 393, 321, 14722, 613, 8000, 13, 639, 1412, 11, 2199, 1412, 11, 445, 337, 22645, 11, 321, 362, 1782, 7901, 13, 492, 362, 1732, 1412, 2793, 11, 1848, 17, 2459, 13, 639, 307, 264, 3218, 295, 1782, 316, 11, 337, 1365, 13, 4928, 363, 3218, 307, 5923, 11, 1360, 13, 440, 661, 472, 307, 6641, 11, 1360, 13, 400, 732, 8078, 362, 264, 912, 3218, 382, 2319, 11, 1360, 13], "avg_logprob": -0.1764081731254672, "compression_ratio": 1.645, "no_speech_prob": 0.0, "words": [{"start": 2271.0, "end": 2271.26, "word": " I", "probability": 0.97265625}, {"start": 2271.26, "end": 2271.4, "word": " will", "probability": 0.8681640625}, {"start": 2271.4, "end": 2271.68, "word": " give", "probability": 0.87255859375}, {"start": 2271.68, "end": 2272.1, "word": " just", "probability": 0.908203125}, {"start": 2272.1, "end": 2272.24, "word": " a", "probability": 0.712890625}, {"start": 2272.24, "end": 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number of houses here, there are five houses, so just three thousand divided by five, six hundred thousand. 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This data is already arranged from largest smallest or smallest large. It doesn't matter actually. So the median is $300,000. Make sense? Because there are two house prices above and two below. So the median is $300,000. 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The mean is double the median. Do you think why there is a big difference in this data between the mean and the median? Which one? Two million dollars is extreme value, very large number.", "tokens": [6915, 11849, 11, 1360, 293, 264, 26779, 307, 6641, 11, 1360, 13, 440, 914, 307, 3834, 264, 26779, 13, 1144, 291, 519, 983, 456, 307, 257, 955, 2649, 294, 341, 1412, 1296, 264, 914, 293, 264, 26779, 30, 3013, 472, 30, 4453, 2459, 3808, 307, 8084, 2158, 11, 588, 2416, 1230, 13], "avg_logprob": -0.17482310758446748, "compression_ratio": 1.464968152866242, "no_speech_prob": 0.0, "words": [{"start": 2358.89, "end": 2359.43, "word": " equals", "probability": 0.53369140625}, {"start": 2359.43, "end": 2359.99, "word": " 600", "probability": 0.7900390625}, {"start": 2359.99, "end": 2360.43, "word": ",000", "probability": 0.831787109375}, {"start": 2360.43, "end": 2361.35, "word": " and", "probability": 0.73681640625}, {"start": 2361.35, "end": 2361.55, "word": " the", "probability": 0.916015625}, {"start": 2361.55, "end": 2361.77, "word": " median", "probability": 0.96728515625}, {"start": 2361.77, "end": 2362.05, "word": " is", "probability": 0.9423828125}, {"start": 2362.05, "end": 2362.47, "word": " 300", "probability": 0.9775390625}, {"start": 2362.47, "end": 2362.97, "word": ",000.", "probability": 0.996337890625}, {"start": 2364.35, "end": 2364.63, "word": " The", "probability": 0.83056640625}, {"start": 2364.63, "end": 2364.79, "word": " mean", "probability": 0.9501953125}, {"start": 2364.79, "end": 2364.97, "word": " is", "probability": 0.9501953125}, {"start": 2364.97, "end": 2365.21, "word": " double", "probability": 0.466552734375}, {"start": 2365.21, "end": 2366.69, "word": " the", "probability": 0.60302734375}, {"start": 2366.69, "end": 2367.05, "word": " median.", "probability": 0.95166015625}, {"start": 2369.11, "end": 2369.75, "word": " Do", "probability": 0.79833984375}, {"start": 2369.75, "end": 2369.81, "word": " you", "probability": 0.9619140625}, {"start": 2369.81, "end": 2370.03, "word": " think", "probability": 0.921875}, {"start": 2370.03, "end": 2370.41, "word": " why", "probability": 0.80126953125}, {"start": 2370.41, "end": 2370.71, "word": " there", "probability": 0.8310546875}, {"start": 2370.71, "end": 2370.85, "word": " is", "probability": 0.92822265625}, {"start": 2370.85, "end": 2370.97, "word": " a", "probability": 0.99609375}, {"start": 2370.97, "end": 2371.15, "word": " big", "probability": 0.92529296875}, {"start": 2371.15, "end": 2371.75, "word": " difference", "probability": 0.87109375}, {"start": 2371.75, "end": 2372.59, "word": " in", "probability": 0.92626953125}, {"start": 2372.59, "end": 2372.85, "word": " this", "probability": 0.94189453125}, {"start": 2372.85, "end": 2373.31, "word": " data", "probability": 0.927734375}, {"start": 2373.31, "end": 2374.81, "word": " between", "probability": 0.8525390625}, {"start": 2374.81, "end": 2375.35, "word": " the", "probability": 0.9267578125}, {"start": 2375.35, "end": 2375.49, "word": " mean", "probability": 0.9716796875}, {"start": 2375.49, "end": 2375.65, "word": " and", "probability": 0.93408203125}, {"start": 2375.65, "end": 2375.77, "word": " the", "probability": 0.888671875}, {"start": 2375.77, "end": 2376.03, "word": " median?", "probability": 0.9482421875}, {"start": 2376.19, "end": 2376.51, "word": " Which", "probability": 0.62109375}, {"start": 2376.51, "end": 2378.13, "word": " one?", "probability": 0.93115234375}, {"start": 2379.37, "end": 2380.01, "word": " Two", "probability": 0.6123046875}, {"start": 2380.01, "end": 2380.27, "word": " million", "probability": 0.8720703125}, {"start": 2380.27, "end": 2380.59, "word": " dollars", "probability": 0.90771484375}, {"start": 2380.59, "end": 2381.23, "word": " is", "probability": 0.197509765625}, {"start": 2381.23, "end": 2381.79, "word": " extreme", "probability": 0.779296875}, {"start": 2381.79, "end": 2382.29, "word": " value,", "probability": 0.97607421875}, {"start": 2382.51, "end": 2382.73, "word": " very", "probability": 0.74951171875}, {"start": 2382.73, "end": 2383.07, "word": " large", "probability": 0.9658203125}, {"start": 2383.07, "end": 2383.41, "word": " number.", "probability": 0.939453125}], "temperature": 1.0}, {"id": 88, "seek": 241214, "start": 2384.32, "end": 2412.14, "text": " I mean, if you compare two million dollars with the other data sets or other data values, you will see there is a big difference between two million and five hundred. It's four times, plus about three hundred thousands, around seven times and so on. For this value, the mean is affected. Exactly. The median is resistant to outliers. 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to use the median. So the median makes more sense than using the mean. The mode is just the most frequent value, which is 100,000, because this value is repeated twice. So that's the whole story for central tendency measures, mean, median, and 1.", "tokens": [1171, 341, 1778, 11, 321, 362, 281, 764, 264, 26779, 13, 407, 264, 26779, 1669, 544, 2020, 813, 1228, 264, 914, 13, 440, 4391, 307, 445, 264, 881, 18004, 2158, 11, 597, 307, 2319, 11, 1360, 11, 570, 341, 2158, 307, 10477, 6091, 13, 407, 300, 311, 264, 1379, 1657, 337, 5777, 18187, 8000, 11, 914, 11, 26779, 11, 293, 502, 13], "avg_logprob": -0.18055555933997744, "compression_ratio": 1.5195530726256983, "no_speech_prob": 0.0, "words": [{"start": 2413.34, "end": 2413.78, "word": " For", "probability": 0.67236328125}, {"start": 2413.78, "end": 2414.02, "word": " this", "probability": 0.93359375}, {"start": 2414.02, "end": 2414.24, "word": " reason,", "probability": 0.95947265625}, {"start": 2414.44, "end": 2415.04, "word": " we", "probability": 0.94482421875}, {"start": 2415.04, "end": 2415.26, "word": " have", "probability": 0.81201171875}, {"start": 2415.26, "end": 2415.44, "word": " to", "probability": 0.96923828125}, {"start": 2415.44, "end": 2415.8, "word": " use", "probability": 0.87548828125}, {"start": 2415.8, "end": 2416.82, "word": " the", "probability": 0.71533203125}, {"start": 2416.82, "end": 2417.1, "word": " median.", "probability": 0.955078125}, {"start": 2417.3, "end": 2417.4, "word": " So", "probability": 0.91357421875}, {"start": 2417.4, "end": 2417.56, "word": " the", "probability": 0.68896484375}, {"start": 2417.56, "end": 2417.76, "word": " median", "probability": 0.96630859375}, {"start": 2417.76, "end": 2418.52, "word": " makes", "probability": 0.84228515625}, {"start": 2418.52, "end": 2418.82, "word": " more", "probability": 0.9375}, {"start": 2418.82, "end": 2419.28, "word": " sense", "probability": 0.83154296875}, {"start": 2419.28, "end": 2420.0, "word": " than", "probability": 0.822265625}, {"start": 2420.0, "end": 2420.44, "word": " using", "probability": 0.9326171875}, {"start": 2420.44, "end": 2420.72, "word": " the", "probability": 0.9130859375}, {"start": 2420.72, "end": 2420.86, "word": " mean.", "probability": 0.97265625}, {"start": 2421.96, "end": 2422.46, "word": " The", "probability": 0.8681640625}, {"start": 2422.46, "end": 2422.68, "word": " mode", "probability": 0.6650390625}, {"start": 2422.68, "end": 2422.92, "word": " is", "probability": 0.943359375}, {"start": 2422.92, "end": 2423.18, "word": " just", "probability": 0.9111328125}, {"start": 2423.18, "end": 2423.38, "word": " the", "probability": 0.90966796875}, {"start": 2423.38, "end": 2423.6, "word": " most", "probability": 0.9013671875}, {"start": 2423.6, "end": 2423.98, "word": " frequent", "probability": 0.89453125}, {"start": 2423.98, "end": 2424.48, "word": " value,", "probability": 0.97607421875}, {"start": 2424.66, "end": 2424.72, "word": " which", "probability": 0.9541015625}, {"start": 2424.72, "end": 2425.0, "word": " is", "probability": 0.9482421875}, {"start": 2425.0, "end": 2425.56, "word": " 100", "probability": 0.66455078125}, {"start": 2425.56, "end": 2426.1, "word": ",000,", "probability": 0.82080078125}, {"start": 2426.38, "end": 2426.84, "word": " because", "probability": 0.90185546875}, {"start": 2426.84, "end": 2427.16, "word": " this", "probability": 0.943359375}, {"start": 2427.16, "end": 2427.52, "word": " value", "probability": 0.97509765625}, {"start": 2427.52, "end": 2428.32, "word": " is", "probability": 0.93603515625}, {"start": 2428.32, "end": 2428.72, "word": " repeated", "probability": 0.96923828125}, {"start": 2428.72, "end": 2429.8, "word": " twice.", "probability": 0.9345703125}, {"start": 2430.94, "end": 2431.5, "word": " So", "probability": 0.94140625}, {"start": 2431.5, "end": 2431.8, "word": " that's", "probability": 0.943359375}, {"start": 2431.8, "end": 2432.04, "word": " the", "probability": 0.9208984375}, {"start": 2432.04, "end": 2432.26, "word": " whole", "probability": 0.88623046875}, {"start": 2432.26, "end": 2432.6, "word": " story", "probability": 0.95556640625}, {"start": 2432.6, "end": 2433.04, "word": " for", "probability": 0.94580078125}, {"start": 2433.04, "end": 2433.82, "word": " central", "probability": 0.83642578125}, {"start": 2433.82, "end": 2434.28, "word": " tendency", "probability": 0.85546875}, {"start": 2434.28, "end": 2434.66, "word": " measures,", "probability": 0.8525390625}, {"start": 2435.14, "end": 2435.4, "word": " mean,", "probability": 0.94580078125}, {"start": 2436.28, "end": 2436.7, "word": " median,", "probability": 0.9677734375}, {"start": 2437.1, "end": 2438.14, "word": " and", "probability": 0.94287109375}, {"start": 2438.14, "end": 2438.34, "word": " 1.", "probability": 0.172119140625}], "temperature": 1.0}, {"id": 90, "seek": 246623, "start": 2440.28, "end": 2466.24, "text": " Now the question again is which measure to use? The mean is generally used. The most common center tendency is the mean. We can use it or we should use it unless extreme values exist. I mean if the data set has no outliers or extreme values, we have to use the mean instead of the median.", "tokens": [823, 264, 1168, 797, 307, 597, 3481, 281, 764, 30, 440, 914, 307, 5101, 1143, 13, 440, 881, 2689, 3056, 18187, 307, 264, 914, 13, 492, 393, 764, 309, 420, 321, 820, 764, 309, 5969, 8084, 4190, 2514, 13, 286, 914, 498, 264, 1412, 992, 575, 572, 484, 23646, 420, 8084, 4190, 11, 321, 362, 281, 764, 264, 914, 2602, 295, 264, 26779, 13], "avg_logprob": -0.1528846153846154, "compression_ratio": 1.6055555555555556, "no_speech_prob": 0.0, "words": [{"start": 2440.28, "end": 2440.54, "word": " Now", "probability": 0.861328125}, {"start": 2440.54, "end": 2440.72, "word": " the", "probability": 0.65478515625}, {"start": 2440.72, "end": 2441.02, "word": " question", "probability": 0.9248046875}, {"start": 2441.02, "end": 2441.44, "word": " again", "probability": 0.9248046875}, {"start": 2441.44, "end": 2441.88, "word": " is", "probability": 0.9306640625}, {"start": 2441.88, "end": 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{"start": 2465.62, "end": 2465.86, "word": " of", "probability": 0.96728515625}, {"start": 2465.86, "end": 2466.02, "word": " the", "probability": 0.92529296875}, {"start": 2466.02, "end": 2466.24, "word": " median.", "probability": 0.68359375}], "temperature": 1.0}, {"id": 91, "seek": 249619, "start": 2469.81, "end": 2496.19, "text": " The median is often used since the median is not sensitive to extreme values. I mean, the median is resistant to outliers. It remains nearly in the same position if the dataset has outliers. But the median will be affected either to the right or to the left tail. So we have to use the median if the data has extreme values.", "tokens": [440, 26779, 307, 2049, 1143, 1670, 264, 26779, 307, 406, 9477, 281, 8084, 4190, 13, 286, 914, 11, 264, 26779, 307, 20383, 281, 484, 23646, 13, 467, 7023, 6217, 294, 264, 912, 2535, 498, 264, 28872, 575, 484, 23646, 13, 583, 264, 26779, 486, 312, 8028, 2139, 281, 264, 558, 420, 281, 264, 1411, 6838, 13, 407, 321, 362, 281, 764, 264, 26779, 498, 264, 1412, 575, 8084, 4190, 13], "avg_logprob": -0.11333626865501135, "compression_ratio": 1.8258426966292134, "no_speech_prob": 0.0, "words": [{"start": 2469.81, "end": 2470.15, "word": " The", "probability": 0.75732421875}, {"start": 2470.15, "end": 2470.43, "word": " median", "probability": 0.96435546875}, {"start": 2470.43, "end": 2471.03, "word": " is", "probability": 0.94677734375}, {"start": 2471.03, "end": 2471.41, "word": " often", "probability": 0.8037109375}, {"start": 2471.41, "end": 2471.91, "word": " used", "probability": 0.92431640625}, {"start": 2471.91, 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So the mean is more sensitive to outliers than the median. Sometimes, I mean in some situations, it makes sense to report both the mean and the median. Just say the mean for this data for home prices is 600,000 while the median is 300,000.", "tokens": [1171, 1365, 11, 26779, 1280, 7901, 337, 264, 3894, 472, 815, 312, 7055, 337, 257, 4458, 300, 307, 1570, 9477, 281, 484, 23646, 13, 407, 264, 914, 307, 544, 9477, 281, 484, 23646, 813, 264, 26779, 13, 4803, 11, 286, 914, 294, 512, 6851, 11, 309, 1669, 2020, 281, 2275, 1293, 264, 914, 293, 264, 26779, 13, 1449, 584, 264, 914, 337, 341, 1412, 337, 1280, 7901, 307, 11849, 11, 1360, 1339, 264, 26779, 307, 6641, 11, 1360, 13], "avg_logprob": -0.14365233946591616, "compression_ratio": 1.7810945273631842, "no_speech_prob": 0.0, "words": [{"start": 2498.58, "end": 2498.88, "word": " For", "probability": 0.87939453125}, {"start": 2498.88, "end": 2499.26, "word": " example,", "probability": 0.96923828125}, {"start": 2499.52, "end": 2499.8, "word": " median", "probability": 0.919921875}, {"start": 2499.8, "end": 2500.06, "word": " home", "probability": 0.76806640625}, {"start": 2500.06, "end": 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So that's all for measures of central tendency. Again, we explained three measures, arithmetic mean, median, and mode. 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denoted by X bar is pronounced as X bar and just summation of X divided by N. So summation Xi, i goes from 1 up to N divided by the total number of observations. The median, as we mentioned, is the value in the middle in ordered array. 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The mode is the most frequent observed value. And we have to know that mean and median are used only for numerical data, while the mode can be used for both numerical and categorical data. That's all about measures of central tendency. Any question?", "tokens": [294, 264, 2808, 13, 440, 4391, 307, 264, 881, 18004, 13095, 2158, 13, 400, 321, 362, 281, 458, 300, 914, 293, 26779, 366, 1143, 787, 337, 29054, 1412, 11, 1339, 264, 4391, 393, 312, 1143, 337, 1293, 29054, 293, 19250, 804, 1412, 13, 663, 311, 439, 466, 8000, 295, 5777, 18187, 13, 2639, 1168, 30], "avg_logprob": -0.16657366284302302, "compression_ratio": 1.5229885057471264, "no_speech_prob": 0.0, "words": [{"start": 2583.09, "end": 2583.37, "word": " in", "probability": 0.380859375}, {"start": 2583.37, "end": 2583.51, "word": " the", "probability": 0.91748046875}, {"start": 2583.51, "end": 2583.73, "word": " middle.", "probability": 0.95263671875}, {"start": 2584.29, "end": 2584.45, "word": " The", "probability": 0.875}, {"start": 2584.45, "end": 2584.75, "word": " mode", "probability": 0.68359375}, {"start": 2584.75, "end": 2585.51, "word": " is", "probability": 0.94677734375}, {"start": 2585.51, "end": 2585.65, "word": " the", "probability": 0.9130859375}, {"start": 2585.65, "end": 2585.87, "word": " most", "probability": 0.90771484375}, {"start": 2585.87, "end": 2586.33, "word": " frequent", "probability": 0.87109375}, {"start": 2586.33, "end": 2586.69, "word": " observed", "probability": 0.84619140625}, {"start": 2586.69, "end": 2587.05, "word": " value.", "probability": 0.9599609375}, {"start": 2587.19, "end": 2587.33, "word": " And", "probability": 0.90283203125}, {"start": 2587.33, "end": 2587.43, "word": " we", "probability": 0.90869140625}, {"start": 2587.43, "end": 2587.57, "word": " have", "probability": 0.94873046875}, {"start": 2587.57, "end": 2587.67, "word": " to", "probability": 0.9716796875}, {"start": 2587.67, "end": 2587.79, "word": " know", "probability": 0.86767578125}, {"start": 2587.79, "end": 2588.09, "word": " that", "probability": 0.93017578125}, {"start": 2588.09, "end": 2588.83, "word": " mean", "probability": 0.8564453125}, {"start": 2588.83, "end": 2589.03, "word": " and", "probability": 0.94140625}, {"start": 2589.03, "end": 2589.33, "word": " median", "probability": 0.974609375}, {"start": 2589.33, "end": 2589.59, "word": " are", "probability": 0.485595703125}, {"start": 2589.59, "end": 2590.43, "word": " used", "probability": 0.927734375}, {"start": 2590.43, "end": 2590.83, "word": " only", "probability": 0.91748046875}, {"start": 2590.83, "end": 2591.17, "word": " for", "probability": 0.9521484375}, {"start": 2591.17, "end": 2591.55, "word": " numerical", "probability": 0.7041015625}, {"start": 2591.55, "end": 2592.13, "word": " data,", "probability": 0.9482421875}, {"start": 2592.83, "end": 2593.61, "word": " while", "probability": 0.95068359375}, {"start": 2593.61, "end": 2593.87, "word": " the", "probability": 0.9228515625}, {"start": 2593.87, "end": 2594.15, "word": " mode", "probability": 0.87890625}, {"start": 2594.15, "end": 2594.45, "word": " can", "probability": 0.9453125}, {"start": 2594.45, "end": 2594.59, "word": " be", "probability": 0.951171875}, {"start": 2594.59, "end": 2594.83, "word": " used", "probability": 0.91162109375}, {"start": 2594.83, "end": 2595.07, "word": " for", "probability": 0.9482421875}, {"start": 2595.07, "end": 2595.47, "word": " both", "probability": 0.89306640625}, {"start": 2595.47, "end": 2596.39, "word": " numerical", "probability": 0.54052734375}, {"start": 2596.39, "end": 2597.51, "word": " and", "probability": 0.947265625}, {"start": 2597.51, "end": 2598.49, "word": " categorical", "probability": 0.853271484375}, {"start": 2598.49, "end": 2598.81, "word": " data.", "probability": 0.92333984375}, {"start": 2600.73, "end": 2601.41, "word": " That's", "probability": 0.9384765625}, {"start": 2601.41, "end": 2601.75, "word": " all", "probability": 0.951171875}, {"start": 2601.75, "end": 2602.35, "word": " about", "probability": 0.90087890625}, {"start": 2602.35, "end": 2603.45, "word": " measures", "probability": 0.478515625}, {"start": 2603.45, "end": 2604.29, "word": " of", "probability": 0.96875}, {"start": 2604.29, "end": 2604.91, "word": " central", "probability": 0.9091796875}, {"start": 2604.91, "end": 2606.13, "word": " tendency.", "probability": 0.9306640625}, {"start": 2606.63, "end": 2606.87, "word": " Any", "probability": 0.91796875}, {"start": 2606.87, "end": 2607.21, "word": " question?", "probability": 0.615234375}], "temperature": 1.0}, {"id": 96, "seek": 264187, "start": 2613.21, "end": 2641.87, "text": " Let's move to measures of variation. It's another type of measures. It's called measures of variation, sometimes called measures of spread. Now, variation can be computed by using range, variance, standard deviation, and coefficient of variation.", "tokens": [961, 311, 1286, 281, 8000, 295, 12990, 13, 467, 311, 1071, 2010, 295, 8000, 13, 467, 311, 1219, 8000, 295, 12990, 11, 2171, 1219, 8000, 295, 3974, 13, 823, 11, 12990, 393, 312, 40610, 538, 1228, 3613, 11, 21977, 11, 3832, 25163, 11, 293, 17619, 295, 12990, 13], "avg_logprob": -0.18223852040816327, "compression_ratio": 1.75177304964539, "no_speech_prob": 0.0, "words": [{"start": 2613.21, "end": 2613.61, "word": " Let's", "probability": 0.7349853515625}, {"start": 2613.61, "end": 2613.99, "word": " move", "probability": 0.93994140625}, {"start": 2613.99, "end": 2616.85, "word": " to", "probability": 0.89892578125}, {"start": 2616.85, "end": 2617.47, "word": " measures", "probability": 0.712890625}, {"start": 2617.47, "end": 2618.27, "word": " of", "probability": 0.96728515625}, {"start": 2618.27, "end": 2619.03, "word": " variation.", "probability": 0.8662109375}, {"start": 2619.71, "end": 2619.85, "word": " It's", "probability": 0.6405029296875}, {"start": 2619.85, "end": 2620.23, "word": " another", "probability": 0.93115234375}, {"start": 2620.23, "end": 2620.75, "word": " type", "probability": 0.974609375}, {"start": 2620.75, "end": 2622.11, "word": " of", "probability": 0.953125}, {"start": 2622.11, "end": 2622.45, "word": " measures.", "probability": 0.57421875}, {"start": 2622.65, "end": 2622.71, "word": " It's", "probability": 0.931396484375}, {"start": 2622.71, "end": 2622.93, "word": " called", "probability": 0.8583984375}, {"start": 2622.93, "end": 2623.29, "word": " measures", "probability": 0.7587890625}, {"start": 2623.29, "end": 2623.75, "word": " of", "probability": 0.96533203125}, {"start": 2623.75, "end": 2624.95, "word": " variation,", "probability": 0.9189453125}, {"start": 2625.53, "end": 2625.95, "word": " sometimes", "probability": 0.94189453125}, {"start": 2625.95, "end": 2626.35, "word": " called", "probability": 0.78857421875}, {"start": 2626.35, "end": 2626.67, "word": " measures", "probability": 0.80126953125}, {"start": 2626.67, "end": 2627.01, "word": " of", "probability": 0.96484375}, {"start": 2627.01, "end": 2627.49, "word": " spread.", "probability": 0.89794921875}, {"start": 2630.49, "end": 2630.79, "word": " Now,", "probability": 0.9208984375}, {"start": 2630.91, "end": 2631.29, "word": " variation", "probability": 0.8779296875}, {"start": 2631.29, "end": 2631.61, "word": " can", "probability": 0.94482421875}, {"start": 2631.61, "end": 2631.79, "word": " be", "probability": 0.95947265625}, {"start": 2631.79, "end": 2632.21, "word": " computed", "probability": 0.9345703125}, {"start": 2632.21, "end": 2632.51, "word": " by", "probability": 0.9609375}, {"start": 2632.51, "end": 2632.89, "word": " using", "probability": 0.94189453125}, {"start": 2632.89, "end": 2633.85, "word": " range,", "probability": 0.8125}, {"start": 2635.59, "end": 2636.25, "word": " variance,", "probability": 0.92236328125}, {"start": 2637.67, "end": 2637.97, "word": " standard", "probability": 0.92822265625}, {"start": 2637.97, "end": 2638.41, "word": " deviation,", "probability": 0.92919921875}, {"start": 2638.99, "end": 2639.35, "word": " and", "probability": 0.9423828125}, {"start": 2639.35, "end": 2639.87, "word": " coefficient", "probability": 0.9150390625}, {"start": 2639.87, "end": 2640.85, "word": " of", "probability": 0.96875}, {"start": 2640.85, "end": 2641.87, "word": " variation.", "probability": 0.85498046875}], "temperature": 1.0}, {"id": 97, "seek": 267121, "start": 2642.27, "end": 2671.21, "text": " So we have four types, range, variance, standard deviation, and coefficient of variation. Now, measures of variation give information on the spread. Now, this is the first difference between central tendency measures and measures of variation. That one measures the central value or the value in the middle. Here, it measures the spread.", "tokens": [407, 321, 362, 1451, 3467, 11, 3613, 11, 21977, 11, 3832, 25163, 11, 293, 17619, 295, 12990, 13, 823, 11, 8000, 295, 12990, 976, 1589, 322, 264, 3974, 13, 823, 11, 341, 307, 264, 700, 2649, 1296, 5777, 18187, 8000, 293, 8000, 295, 12990, 13, 663, 472, 8000, 264, 5777, 2158, 420, 264, 2158, 294, 264, 2808, 13, 1692, 11, 309, 8000, 264, 3974, 13], "avg_logprob": -0.14618844696969696, "compression_ratio": 1.7883597883597884, "no_speech_prob": 0.0, "words": [{"start": 2642.27, "end": 2642.55, "word": " So", "probability": 0.869140625}, {"start": 2642.55, "end": 2642.69, "word": " we", "probability": 0.75}, {"start": 2642.69, "end": 2642.99, "word": " have", "probability": 0.95068359375}, {"start": 2642.99, "end": 2644.23, "word": " four", "probability": 0.865234375}, {"start": 2644.23, "end": 2645.79, "word": " types,", "probability": 0.818359375}, {"start": 2646.07, "end": 2646.51, "word": " range,", "probability": 0.79541015625}, {"start": 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"text": " Or variability. Or dispersion of the data. Do you know what is dispersion? Dispersion. Tabaad. So major variation given formation with the spread. Spread or variation or dispersion of the data values. Now if you look at these two bell shapes. Both have the same center. The center I mean the value in the middle.", "tokens": [1610, 35709, 13, 1610, 24631, 313, 295, 264, 1412, 13, 1144, 291, 458, 437, 307, 24631, 313, 30, 4208, 21819, 313, 13, 14106, 64, 345, 13, 407, 2563, 12990, 2212, 11723, 365, 264, 3974, 13, 30308, 420, 12990, 420, 24631, 313, 295, 264, 1412, 4190, 13, 823, 498, 291, 574, 412, 613, 732, 4549, 10854, 13, 6767, 362, 264, 912, 3056, 13, 440, 3056, 286, 914, 264, 2158, 294, 264, 2808, 13], "avg_logprob": -0.2724743118024852, "compression_ratio": 1.7197802197802199, "no_speech_prob": 0.0, "words": [{"start": 2671.55, "end": 2671.97, "word": " Or", "probability": 0.52783203125}, {"start": 2671.97, "end": 2672.57, "word": " variability.", "probability": 0.95361328125}, {"start": 2674.13, "end": 2674.71, "word": " Or", "probability": 0.9716796875}, {"start": 2674.71, "end": 2675.45, "word": " dispersion", "probability": 0.9423828125}, {"start": 2675.45, "end": 2675.89, "word": " of", "probability": 0.9609375}, {"start": 2675.89, "end": 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So both graphs have the same center. But if you look at the spread, you will see that figure A is less spread than figure B. Now if you look at this one, the spread here,", "tokens": [407, 264, 2158, 294, 264, 2808, 510, 337, 2573, 4295, 1230, 472, 307, 264, 912, 382, 264, 2158, 337, 264, 661, 4295, 13, 407, 1293, 24877, 362, 264, 912, 3056, 13, 583, 498, 291, 574, 412, 264, 3974, 11, 291, 486, 536, 300, 2573, 316, 307, 1570, 3974, 813, 2573, 363, 13, 823, 498, 291, 574, 412, 341, 472, 11, 264, 3974, 510, 11], "avg_logprob": -0.15264423076923078, "compression_ratio": 1.720496894409938, "no_speech_prob": 0.0, "words": [{"start": 2700.17, "end": 2700.69, "word": " So", "probability": 0.8623046875}, {"start": 2700.69, "end": 2701.05, "word": " the", "probability": 0.65966796875}, {"start": 2701.05, "end": 2701.25, "word": " value", "probability": 0.97314453125}, {"start": 2701.25, "end": 2701.39, "word": " in", "probability": 0.93896484375}, {"start": 2701.39, "end": 2701.51, "word": " the", "probability": 0.919921875}, {"start": 2701.51, "end": 2701.73, "word": " middle", "probability": 0.95458984375}, 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So I mean,", "tokens": [420, 3974, 484, 294, 1508, 316, 1310, 709, 544, 813, 294, 1508, 363, 13, 407, 264, 914, 307, 406, 11563, 281, 6786, 264, 1412, 13, 509, 362, 281, 584, 300, 264, 914, 6915, 1270, 293, 1270, 293, 264, 3974, 13, 400, 472, 295, 613, 8000, 321, 603, 751, 1780, 466, 3613, 293, 21977, 3832, 25163, 13, 407, 286, 914, 11], "avg_logprob": -0.17213114460960763, "compression_ratio": 1.5593220338983051, "no_speech_prob": 0.0, "words": [{"start": 2785.84, "end": 2786.12, "word": " or", "probability": 0.58740234375}, {"start": 2786.12, "end": 2786.64, "word": " spread", "probability": 0.90185546875}, {"start": 2786.64, "end": 2787.2, "word": " out", "probability": 0.88818359375}, {"start": 2787.2, "end": 2787.9, "word": " in", "probability": 0.8876953125}, {"start": 2787.9, "end": 2788.3, "word": " class", "probability": 0.53271484375}, {"start": 2788.3, "end": 2788.66, "word": " A", "probability": 0.873046875}, {"start": 2788.66, "end": 2789.16, "word": " maybe", 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is not sufficient to describe the data. You have to use something else to measure the variation or the spread of the data. Make sense? The first measure of variation, the easiest one, is called the range. The range is the simplest measure of variation.", "tokens": [440, 914, 538, 2564, 307, 406, 11563, 281, 6786, 264, 1412, 13, 509, 362, 281, 764, 746, 1646, 281, 3481, 264, 12990, 420, 264, 3974, 295, 264, 1412, 13, 4387, 2020, 30, 440, 700, 3481, 295, 12990, 11, 264, 12889, 472, 11, 307, 1219, 264, 3613, 13, 440, 3613, 307, 264, 22811, 3481, 295, 12990, 13], "avg_logprob": -0.12842653927050138, "compression_ratio": 1.6790123456790123, "no_speech_prob": 0.0, "words": [{"start": 2807.19, "end": 2807.49, "word": " The", "probability": 0.79638671875}, {"start": 2807.49, "end": 2807.67, "word": " mean", "probability": 0.96435546875}, {"start": 2807.67, "end": 2807.91, "word": " by", "probability": 0.9267578125}, {"start": 2807.91, "end": 2808.41, "word": " itself", "probability": 0.8515625}, {"start": 2808.41, "end": 2808.83, "word": " is", "probability": 0.93017578125}, {"start": 2808.83, "end": 2809.03, "word": " not", "probability": 0.9482421875}, {"start": 2809.03, "end": 2809.39, "word": " sufficient", "probability": 0.8427734375}, {"start": 2809.39, "end": 2809.77, "word": " to", "probability": 0.97021484375}, {"start": 2809.77, "end": 2810.21, "word": " describe", "probability": 0.90771484375}, {"start": 2810.21, "end": 2810.39, "word": " the", "probability": 0.89306640625}, {"start": 2810.39, "end": 2810.63, "word": " data.", "probability": 0.95068359375}, {"start": 2811.23, "end": 2811.33, "word": " You", "probability": 0.95751953125}, {"start": 2811.33, "end": 2811.57, "word": " have", "probability": 0.94775390625}, {"start": 2811.57, "end": 2811.69, "word": " to", "probability": 0.96875}, {"start": 2811.69, "end": 2811.89, "word": " use", "probability": 0.88232421875}, {"start": 2811.89, "end": 2812.29, "word": " something", "probability": 0.86328125}, {"start": 2812.29, "end": 2812.83, "word": " else", "probability": 0.9306640625}, {"start": 2812.83, "end": 2813.65, "word": " to", "probability": 0.953125}, {"start": 2813.65, "end": 2814.03, "word": " measure", "probability": 0.8818359375}, {"start": 2814.03, "end": 2814.77, "word": " the", "probability": 0.9052734375}, {"start": 2814.77, "end": 2815.19, "word": " variation", "probability": 0.93505859375}, {"start": 2815.19, "end": 2815.55, "word": " or", "probability": 0.89501953125}, {"start": 2815.55, "end": 2815.73, "word": " the", "probability": 0.91015625}, {"start": 2815.73, "end": 2816.09, "word": " spread", "probability": 0.9052734375}, {"start": 2816.09, "end": 2816.35, "word": " of", "probability": 0.96875}, {"start": 2816.35, "end": 2816.49, "word": " the", "probability": 0.91455078125}, {"start": 2816.49, "end": 2816.77, "word": " data.", "probability": 0.9326171875}, {"start": 2817.47, "end": 2817.65, "word": " Make", "probability": 0.77880859375}, {"start": 2817.65, "end": 2817.95, "word": " sense?", "probability": 0.8408203125}, {"start": 2822.17, "end": 2822.77, "word": " The", "probability": 0.791015625}, {"start": 2822.77, "end": 2823.13, "word": " first", "probability": 0.89208984375}, {"start": 2823.13, "end": 2823.41, "word": " measure", "probability": 0.8681640625}, {"start": 2823.41, "end": 2823.59, "word": " of", "probability": 0.96435546875}, {"start": 2823.59, "end": 2824.01, "word": " variation,", "probability": 0.9091796875}, {"start": 2824.81, "end": 2824.93, "word": " the", "probability": 0.91943359375}, {"start": 2824.93, "end": 2825.23, "word": " easiest", "probability": 0.90234375}, {"start": 2825.23, "end": 2825.67, "word": " one,", "probability": 0.9267578125}, {"start": 2825.81, "end": 2825.87, "word": " is", "probability": 0.9404296875}, {"start": 2825.87, "end": 2826.15, "word": " called", "probability": 0.91650390625}, {"start": 2826.15, "end": 2826.37, "word": " the", "probability": 0.7861328125}, {"start": 2826.37, "end": 2826.65, "word": " range.", "probability": 0.7666015625}, {"start": 2828.67, "end": 2828.89, "word": " The", "probability": 0.83740234375}, {"start": 2828.89, "end": 2829.25, "word": " range", "probability": 0.89453125}, {"start": 2829.25, "end": 2830.85, "word": " is", "probability": 0.7490234375}, {"start": 2830.85, "end": 2830.93, "word": " the", "probability": 0.54443359375}, {"start": 2830.93, "end": 2831.23, "word": " simplest", "probability": 0.90185546875}, {"start": 2831.23, "end": 2831.59, "word": " measure", "probability": 0.857421875}, {"start": 2831.59, "end": 2831.77, "word": " of", "probability": 0.9658203125}, {"start": 2831.77, "end": 2832.09, "word": " variation.", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 104, "seek": 286349, "start": 2834.21, "end": 2863.49, "text": " The range is just the difference or the distance between the largest and the smallest value. For example, suppose the minimum score for this class is 40 and the maximum is 90. So the range is 50, 90 minus 40. Now imagine that the minimum score for this class is 60 and the maximum is 80, so 20.", "tokens": [440, 3613, 307, 445, 264, 2649, 420, 264, 4560, 1296, 264, 6443, 293, 264, 16998, 2158, 13, 1171, 1365, 11, 7297, 264, 7285, 6175, 337, 341, 1508, 307, 3356, 293, 264, 6674, 307, 4289, 13, 407, 264, 3613, 307, 2625, 11, 4289, 3175, 3356, 13, 823, 3811, 300, 264, 7285, 6175, 337, 341, 1508, 307, 4060, 293, 264, 6674, 307, 4688, 11, 370, 945, 13], "avg_logprob": -0.12736742582285043, "compression_ratio": 1.755952380952381, "no_speech_prob": 0.0, "words": [{"start": 2834.21, "end": 2834.47, "word": " The", "probability": 0.69091796875}, {"start": 2834.47, "end": 2834.71, "word": " range", "probability": 0.84765625}, {"start": 2834.71, "end": 2834.91, "word": " is", "probability": 0.9375}, {"start": 2834.91, "end": 2835.35, "word": " just", "probability": 0.90576171875}, {"start": 2835.35, "end": 2835.59, "word": " the", "probability": 0.90869140625}, {"start": 2835.59, "end": 2836.15, 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That means a range is affected by outliers because it depends only on two values.", "tokens": [759, 321, 7406, 4688, 538, 2319, 11, 286, 914, 264, 7285, 307, 4060, 293, 264, 6674, 307, 2319, 11, 309, 311, 3356, 13, 663, 1355, 257, 3613, 307, 8028, 538, 484, 23646, 570, 309, 5946, 787, 322, 732, 4190, 13], "avg_logprob": -0.19988567363925097, "compression_ratio": 1.2790697674418605, "no_speech_prob": 0.0, "words": [{"start": 2865.85, "end": 2866.13, "word": " If", "probability": 0.78173828125}, {"start": 2866.13, "end": 2866.33, "word": " we", "probability": 0.95166015625}, {"start": 2866.33, "end": 2866.75, "word": " replace", "probability": 0.39990234375}, {"start": 2866.75, "end": 2867.33, "word": " 80", "probability": 0.9208984375}, {"start": 2867.33, "end": 2867.81, "word": " by", "probability": 0.9580078125}, {"start": 2867.81, "end": 2868.31, "word": " 100,", "probability": 0.91357421875}, {"start": 2869.05, "end": 2869.17, "word": " I", "probability": 0.91162109375}, {"start": 2869.17, "end": 2869.25, "word": " mean", "probability": 0.9677734375}, {"start": 2869.25, "end": 2869.39, "word": " the", "probability": 0.6572265625}, {"start": 2869.39, "end": 2869.59, "word": " minimum", "probability": 0.9814453125}, {"start": 2869.59, "end": 2869.79, "word": " is", "probability": 0.93701171875}, {"start": 2869.79, "end": 2870.21, "word": " 60", "probability": 0.974609375}, {"start": 2870.21, "end": 2871.03, "word": " and", "probability": 0.6259765625}, {"start": 2871.03, "end": 2871.17, "word": " the", "probability": 0.9033203125}, {"start": 2871.17, "end": 2871.45, "word": " maximum", "probability": 0.93994140625}, {"start": 2871.45, "end": 2871.61, "word": " is", "probability": 0.947265625}, {"start": 2871.61, "end": 2872.11, "word": " 100,", "probability": 0.8203125}, {"start": 2872.51, "end": 2873.07, "word": " it's", "probability": 0.729736328125}, {"start": 2873.07, "end": 2873.55, "word": " 40.", "probability": 0.9697265625}, {"start": 2874.37, "end": 2874.75, "word": " That", "probability": 0.8388671875}, {"start": 2874.75, "end": 2875.21, "word": " means", "probability": 0.94189453125}, {"start": 2875.21, "end": 2875.55, "word": " a", "probability": 0.443115234375}, {"start": 2875.55, "end": 2875.93, "word": " range", "probability": 0.90283203125}, {"start": 2875.93, "end": 2876.31, "word": " is", "probability": 0.94482421875}, {"start": 2876.31, "end": 2876.75, "word": " affected", "probability": 0.86572265625}, {"start": 2876.75, "end": 2877.03, "word": " by", "probability": 0.9697265625}, {"start": 2877.03, "end": 2877.45, "word": " outliers", "probability": 0.705078125}, {"start": 2877.45, "end": 2880.39, "word": " because", "probability": 0.410888671875}, {"start": 2880.39, "end": 2880.63, "word": " it", "probability": 0.94384765625}, {"start": 2880.63, "end": 2880.95, "word": " depends", "probability": 0.92919921875}, {"start": 2880.95, "end": 2881.35, "word": " only", "probability": 0.90283203125}, {"start": 2881.35, "end": 2881.55, "word": " on", "probability": 0.8837890625}, {"start": 2881.55, "end": 2881.69, "word": " two", "probability": 0.90380859375}, {"start": 2881.69, "end": 2882.17, "word": " values.", "probability": 0.974609375}], "temperature": 1.0}, {"id": 106, "seek": 290936, "start": 2883.48, "end": 2909.36, "text": " maximum and minimum value. So it should be affected by outliers. So range is sensitive to outliers. So if the data has the data set has outliers, then in this case, you have to avoid using range because range only based on two values. So it should be affected by outliers. Now for the for simple example, suppose we have this data. The minimum value is one.", "tokens": [6674, 293, 7285, 2158, 13, 407, 309, 820, 312, 8028, 538, 484, 23646, 13, 407, 3613, 307, 9477, 281, 484, 23646, 13, 407, 498, 264, 1412, 575, 264, 1412, 992, 575, 484, 23646, 11, 550, 294, 341, 1389, 11, 291, 362, 281, 5042, 1228, 3613, 570, 3613, 787, 2361, 322, 732, 4190, 13, 407, 309, 820, 312, 8028, 538, 484, 23646, 13, 823, 337, 264, 337, 2199, 1365, 11, 7297, 321, 362, 341, 1412, 13, 440, 7285, 2158, 307, 472, 13], "avg_logprob": -0.1763529007027789, "compression_ratio": 1.8842105263157896, "no_speech_prob": 0.0, "words": [{"start": 2883.48, "end": 2884.04, "word": " maximum", "probability": 0.7216796875}, {"start": 2884.04, "end": 2884.6, "word": " and", "probability": 0.91162109375}, {"start": 2884.6, "end": 2884.9, "word": " minimum", "probability": 0.958984375}, {"start": 2884.9, "end": 2885.28, "word": " value.", "probability": 0.654296875}, {"start": 2885.42, "end": 2885.54, "word": " So", "probability": 0.91552734375}, {"start": 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It becomes now 99 after we replace the maximum by 100. So it means that range is affected by extreme values. So the mean and range both are sensitive to outliers. 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Mean and range are affected by outliers. The mean and range are affected by outliers. This is an example. So it's very easy to compute the mean. Next, if you look at why the range can be misleading.", "tokens": [8000, 295, 3056, 18187, 293, 8000, 295, 12990, 13, 12302, 293, 3613, 366, 8028, 538, 484, 23646, 13, 440, 914, 293, 3613, 366, 8028, 538, 484, 23646, 13, 639, 307, 364, 1365, 13, 407, 309, 311, 588, 1858, 281, 14722, 264, 914, 13, 3087, 11, 498, 291, 574, 412, 983, 264, 3613, 393, 312, 36429, 13], "avg_logprob": -0.14775219298245615, "compression_ratio": 1.6493506493506493, "no_speech_prob": 0.0, "words": [{"start": 2966.41, "end": 2967.17, "word": " measures", "probability": 0.433837890625}, {"start": 2967.17, "end": 2967.59, "word": " of", "probability": 0.96142578125}, {"start": 2967.59, "end": 2967.85, "word": " center", "probability": 0.6396484375}, {"start": 2967.85, "end": 2968.31, "word": " tendency", "probability": 0.74853515625}, {"start": 2968.31, "end": 2969.29, "word": " and", "probability": 0.6875}, {"start": 2969.29, "end": 2969.67, "word": " measures", "probability": 0.8203125}, {"start": 2969.67, "end": 2970.21, "word": " of", "probability": 0.96728515625}, {"start": 2970.21, "end": 2970.87, "word": " variation.", "probability": 0.86669921875}, {"start": 2971.69, "end": 2971.79, "word": " Mean", "probability": 0.9287109375}, {"start": 2971.79, "end": 2971.99, "word": " and", "probability": 0.947265625}, {"start": 2971.99, "end": 2972.25, "word": " range", "probability": 0.8642578125}, {"start": 2972.25, "end": 2972.47, "word": " are", "probability": 0.9404296875}, {"start": 2972.47, "end": 2972.87, "word": " affected", "probability": 0.8779296875}, {"start": 2972.87, "end": 2973.13, "word": " by", "probability": 0.96923828125}, {"start": 2973.13, "end": 2973.61, "word": " outliers.", "probability": 0.943359375}, {"start": 2974.43, "end": 2975.05, "word": " The", "probability": 0.73095703125}, {"start": 2975.05, "end": 2975.23, "word": " mean", "probability": 0.96435546875}, {"start": 2975.23, "end": 2975.43, "word": " and", "probability": 0.93359375}, {"start": 2975.43, "end": 2976.91, "word": " range", "probability": 0.75}, {"start": 2976.91, "end": 2977.11, "word": " are", "probability": 0.92822265625}, {"start": 2977.11, "end": 2977.47, "word": " affected", "probability": 0.8701171875}, {"start": 2977.47, "end": 2977.91, "word": " by", "probability": 0.96875}, {"start": 2977.91, "end": 2978.65, "word": " outliers.", "probability": 0.927490234375}, {"start": 2978.79, "end": 2978.87, "word": " This", "probability": 0.63427734375}, {"start": 2978.87, "end": 2979.03, "word": " is", "probability": 0.943359375}, {"start": 2979.03, "end": 2979.23, "word": " an", "probability": 0.9580078125}, {"start": 2979.23, "end": 2979.87, "word": " example.", "probability": 0.95849609375}, {"start": 2980.23, "end": 2980.33, "word": " So", "probability": 0.83837890625}, {"start": 2980.33, "end": 2980.77, "word": " it's", "probability": 0.701904296875}, {"start": 2980.77, "end": 2980.99, "word": " very", "probability": 0.84375}, {"start": 2980.99, "end": 2981.25, "word": " easy", "probability": 0.91064453125}, {"start": 2981.25, "end": 2981.45, "word": " to", "probability": 0.970703125}, {"start": 2981.45, "end": 2981.77, "word": " compute", "probability": 0.86767578125}, {"start": 2981.77, "end": 2981.95, "word": " the", "probability": 0.921875}, {"start": 2981.95, "end": 2982.15, "word": " mean.", "probability": 0.9638671875}, {"start": 2984.15, "end": 2984.67, "word": " Next,", "probability": 0.92822265625}, {"start": 2985.61, "end": 2986.01, "word": " if", "probability": 0.943359375}, {"start": 2986.01, "end": 2986.09, "word": " you", "probability": 0.947265625}, {"start": 2986.09, "end": 2986.27, "word": " look", "probability": 0.96826171875}, {"start": 2986.27, "end": 2987.29, "word": " at", "probability": 0.9697265625}, {"start": 2987.29, "end": 2989.33, "word": " why", "probability": 0.900390625}, {"start": 2989.33, "end": 2989.55, "word": " the", "probability": 0.9228515625}, {"start": 2989.55, "end": 2989.97, "word": " range", "probability": 0.8935546875}, {"start": 2989.97, "end": 2990.51, "word": " can", "probability": 0.94482421875}, {"start": 2990.51, "end": 2990.71, "word": " be", "probability": 0.96044921875}, {"start": 2990.71, "end": 2991.19, "word": " misleading.", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 110, "seek": 302249, "start": 2993.83, "end": 3022.49, "text": " Sometimes you report the range and the range does not give an appropriate answer or appropriate result because number one ignores the way in which the data are distributed. For example, if you look at this specific data, we have data seven, eight, nine, ten, eleven and twelve. So the range is five. Twelve minus seven is five. Now if you look at the other data,", "tokens": [4803, 291, 2275, 264, 3613, 293, 264, 3613, 775, 406, 976, 364, 6854, 1867, 420, 6854, 1874, 570, 1230, 472, 5335, 2706, 264, 636, 294, 597, 264, 1412, 366, 12631, 13, 1171, 1365, 11, 498, 291, 574, 412, 341, 2685, 1412, 11, 321, 362, 1412, 3407, 11, 3180, 11, 4949, 11, 2064, 11, 21090, 293, 14390, 13, 407, 264, 3613, 307, 1732, 13, 48063, 3175, 3407, 307, 1732, 13, 823, 498, 291, 574, 412, 264, 661, 1412, 11], "avg_logprob": -0.16327135585531405, "compression_ratio": 1.736842105263158, "no_speech_prob": 0.0, "words": [{"start": 2993.83, "end": 2994.35, "word": " Sometimes", "probability": 0.51318359375}, {"start": 2994.35, "end": 2994.87, "word": " you", "probability": 0.71728515625}, {"start": 2994.87, "end": 2995.19, "word": " report", "probability": 0.95458984375}, {"start": 2995.19, "end": 2995.39, "word": " the", "probability": 0.7333984375}, {"start": 2995.39, "end": 2995.69, "word": " range", "probability": 0.9130859375}, 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And there is a gap between the smallest and the next smallest value, which is 10. And also we have 12 is repeated three times. Still the range is the same. Even there is a difference between these two values, between two sets.", "tokens": [440, 16998, 2158, 390, 3407, 13, 400, 456, 307, 257, 7417, 1296, 264, 16998, 293, 264, 958, 16998, 2158, 11, 597, 307, 1266, 13, 400, 611, 321, 362, 2272, 307, 10477, 1045, 1413, 13, 8291, 264, 3613, 307, 264, 912, 13, 2754, 456, 307, 257, 2649, 1296, 613, 732, 4190, 11, 1296, 732, 6352, 13], "avg_logprob": -0.137904572433659, "compression_ratio": 1.6688311688311688, "no_speech_prob": 0.0, "words": [{"start": 3024.72, "end": 3025.0, "word": " The", "probability": 0.7373046875}, {"start": 3025.0, "end": 3025.38, "word": " smallest", "probability": 0.939453125}, {"start": 3025.38, "end": 3025.66, "word": " value", "probability": 0.97802734375}, {"start": 3025.66, "end": 3025.9, "word": " was", "probability": 0.93994140625}, {"start": 3025.9, "end": 3026.36, "word": " seven.", "probability": 0.76220703125}, {"start": 3029.6, "end": 3030.28, "word": " And", "probability": 0.7236328125}, {"start": 3030.28, "end": 3030.48, "word": " there", "probability": 0.90966796875}, {"start": 3030.48, "end": 3030.62, "word": " is", "probability": 0.91064453125}, {"start": 3030.62, "end": 3030.8, "word": " a", "probability": 0.95703125}, {"start": 3030.8, "end": 3031.06, "word": " gap", "probability": 0.9599609375}, {"start": 3031.06, "end": 3031.5, "word": " between", "probability": 0.8515625}, {"start": 3031.5, "end": 3032.08, "word": " the", "probability": 0.88427734375}, {"start": 3032.08, "end": 3032.6, "word": " smallest", "probability": 0.93212890625}, {"start": 3032.6, "end": 3033.08, "word": " and", "probability": 0.92041015625}, {"start": 3033.08, "end": 3033.26, "word": " the", "probability": 0.90625}, {"start": 3033.26, "end": 3033.5, "word": " next", "probability": 0.9150390625}, {"start": 3033.5, "end": 3033.96, "word": " smallest", "probability": 0.9453125}, {"start": 3033.96, "end": 3034.5, "word": " value,", "probability": 0.97119140625}, {"start": 3034.9, "end": 3035.26, "word": " which", "probability": 0.94384765625}, {"start": 3035.26, "end": 3035.5, "word": " is", "probability": 0.93798828125}, {"start": 3035.5, "end": 3035.84, "word": " 10.", "probability": 0.662109375}, {"start": 3037.18, "end": 3037.52, "word": " And", "probability": 0.9326171875}, {"start": 3037.52, "end": 3037.76, "word": " also", "probability": 0.826171875}, {"start": 3037.76, "end": 3037.92, "word": " we", "probability": 0.63525390625}, {"start": 3037.92, "end": 3038.22, "word": " have", "probability": 0.94677734375}, {"start": 3038.22, "end": 3039.3, "word": " 12", "probability": 0.837890625}, {"start": 3039.3, "end": 3039.6, "word": " is", "probability": 0.77734375}, {"start": 3039.6, "end": 3039.92, "word": " repeated", "probability": 0.95458984375}, {"start": 3039.92, "end": 3040.24, "word": " three", "probability": 0.9248046875}, {"start": 3040.24, "end": 3040.68, "word": " times.", "probability": 0.92578125}, {"start": 3042.12, "end": 3042.58, "word": " Still", "probability": 0.9326171875}, {"start": 3042.58, "end": 3042.78, "word": " the", "probability": 0.548828125}, {"start": 3042.78, "end": 3043.18, "word": " range", "probability": 0.8798828125}, {"start": 3043.18, "end": 3044.28, "word": " is", "probability": 0.94189453125}, {"start": 3044.28, "end": 3044.48, "word": " the", "probability": 0.91015625}, {"start": 3044.48, "end": 3044.74, "word": " same.", "probability": 0.9052734375}, {"start": 3045.34, "end": 3045.68, "word": " Even", "probability": 0.86865234375}, {"start": 3045.68, "end": 3046.52, "word": " there", "probability": 0.80712890625}, {"start": 3046.52, "end": 3046.68, "word": " is", "probability": 0.93798828125}, {"start": 3046.68, "end": 3046.86, "word": " a", "probability": 0.998046875}, {"start": 3046.86, "end": 3047.24, "word": " difference", "probability": 0.875}, {"start": 3047.24, "end": 3047.64, "word": " between", "probability": 0.8701171875}, {"start": 3047.64, "end": 3047.96, "word": " these", "probability": 0.8623046875}, {"start": 3047.96, "end": 3048.14, "word": " two", "probability": 0.93408203125}, {"start": 3048.14, "end": 3048.6, "word": " values,", "probability": 0.96923828125}, {"start": 3049.8, "end": 3050.22, "word": " between", "probability": 0.8818359375}, {"start": 3050.22, "end": 3050.44, "word": " two", "probability": 0.9267578125}, {"start": 3050.44, "end": 3050.78, "word": " sets.", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 112, "seek": 307836, "start": 3051.52, "end": 3078.36, "text": " we have seven, eight, nine up to 12. And then the other data, we have seven, 10, 11, and 12 three times. Still, the range equals five. So it doesn't make sense to report the range as a measure of variation. Because if you look at the distribution for this data, it's completely different from the other dataset. 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So range is not used in this case. Look at another example. We have data. All the data ranges, I mean, starts from 1 up to 5. So the range is 4. If we just replace the maximum, which is 5, by 120. So the range is completely different.", "tokens": [264, 912, 3613, 13, 407, 3613, 307, 406, 1143, 294, 341, 1389, 13, 2053, 412, 1071, 1365, 13, 492, 362, 1412, 13, 1057, 264, 1412, 22526, 11, 286, 914, 11, 3719, 490, 502, 493, 281, 1025, 13, 407, 264, 3613, 307, 1017, 13, 759, 321, 445, 7406, 264, 6674, 11, 597, 307, 1025, 11, 538, 10411, 13, 407, 264, 3613, 307, 2584, 819, 13], "avg_logprob": -0.15685096153846154, "compression_ratio": 1.4593023255813953, "no_speech_prob": 0.0, "words": [{"start": 3079.28, "end": 3079.54, "word": " the", "probability": 0.45751953125}, {"start": 3079.54, "end": 3079.94, "word": " same", "probability": 0.896484375}, {"start": 3079.94, "end": 3080.54, "word": " range.", "probability": 0.86669921875}, {"start": 3080.8, "end": 3080.86, "word": " So", "probability": 0.83935546875}, {"start": 3080.86, "end": 3082.24, "word": " range", "probability": 0.72265625}, {"start": 3082.24, "end": 3082.42, "word": " is", "probability": 0.9462890625}, {"start": 3082.42, "end": 3082.62, "word": " not", "probability": 0.951171875}, {"start": 3082.62, "end": 3082.92, "word": " used", "probability": 0.92236328125}, {"start": 3082.92, "end": 3083.1, "word": " in", "probability": 0.94677734375}, {"start": 3083.1, "end": 3083.36, "word": " this", "probability": 0.94775390625}, {"start": 3083.36, "end": 3083.7, "word": " case.", "probability": 0.91259765625}, {"start": 3084.4, "end": 3084.74, "word": " Look", "probability": 0.830078125}, {"start": 3084.74, "end": 3084.86, "word": " at", "probability": 0.96728515625}, {"start": 3084.86, "end": 3085.22, "word": " another", "probability": 0.7939453125}, {"start": 3085.22, "end": 3085.68, "word": " example.", "probability": 0.9697265625}, {"start": 3088.3, "end": 3088.98, "word": " We", "probability": 0.95556640625}, {"start": 3088.98, "end": 3089.14, "word": " have", "probability": 0.9443359375}, {"start": 3089.14, "end": 3089.48, "word": " data.", "probability": 0.943359375}, {"start": 3090.12, "end": 3090.32, "word": " All", "probability": 0.9755859375}, {"start": 3090.32, "end": 3090.44, "word": " the", "probability": 0.91015625}, {"start": 3090.44, "end": 3090.72, "word": " data", "probability": 0.94091796875}, {"start": 3090.72, "end": 3091.26, "word": " ranges,", "probability": 0.5947265625}, {"start": 3091.98, "end": 3092.38, "word": " I", "probability": 0.912109375}, {"start": 3092.38, "end": 3092.52, "word": " mean,", "probability": 0.9677734375}, {"start": 3092.58, "end": 3092.92, "word": " starts", "probability": 0.78759765625}, {"start": 3092.92, "end": 3093.16, "word": " from", "probability": 0.89501953125}, {"start": 3093.16, "end": 3093.4, "word": " 1", "probability": 0.43017578125}, {"start": 3093.4, "end": 3093.58, "word": " up", "probability": 0.96240234375}, {"start": 3093.58, "end": 3093.7, "word": " to", "probability": 0.9658203125}, {"start": 3093.7, "end": 3094.08, "word": " 5.", "probability": 0.98095703125}, {"start": 3094.64, "end": 3095.0, "word": " So", "probability": 0.9638671875}, {"start": 3095.0, "end": 3095.16, "word": " the", "probability": 0.89501953125}, {"start": 3095.16, "end": 3095.48, "word": " range", "probability": 0.892578125}, {"start": 3095.48, "end": 3095.9, "word": " is", "probability": 0.94482421875}, {"start": 3095.9, "end": 3096.24, "word": " 4.", "probability": 0.92724609375}, {"start": 3097.88, "end": 3098.12, "word": " If", "probability": 0.95654296875}, {"start": 3098.12, "end": 3098.3, "word": " we", "probability": 0.9599609375}, {"start": 3098.3, "end": 3098.68, "word": " just", "probability": 0.92236328125}, {"start": 3098.68, "end": 3099.28, "word": " replace", "probability": 0.84375}, {"start": 3099.28, "end": 3100.28, "word": " the", "probability": 0.90478515625}, {"start": 3100.28, "end": 3100.76, "word": " maximum,", "probability": 0.93798828125}, {"start": 3101.28, "end": 3101.58, "word": " which", "probability": 0.94580078125}, {"start": 3101.58, "end": 3101.74, "word": " is", "probability": 0.94873046875}, {"start": 3101.74, "end": 3102.14, "word": " 5,", "probability": 0.9775390625}, {"start": 3102.36, "end": 3103.0, "word": " by", "probability": 0.96826171875}, {"start": 3103.0, "end": 3103.52, "word": " 120.", "probability": 0.93701171875}, {"start": 3105.64, "end": 3106.0, "word": " So", "probability": 0.94873046875}, {"start": 3106.0, "end": 3106.2, "word": " the", "probability": 0.91064453125}, {"start": 3106.2, "end": 3106.52, "word": " range", "probability": 0.87646484375}, {"start": 3106.52, "end": 3106.82, "word": " is", "probability": 0.94873046875}, {"start": 3106.82, "end": 3107.46, "word": " completely", "probability": 0.74951171875}, {"start": 3107.46, "end": 3107.82, "word": " different.", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 114, "seek": 313625, "start": 3108.39, "end": 3136.25, "text": " the range becomes 119. So that means range is sensitive to outliers. So we have to avoid using range in case of outliers or extreme values. 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Okay, stop at this point if you have any question. 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