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Mean and median are 2 of the most basic statistical concepts, and they're foundational to other, more complicated concepts. The mean is the average of a set of numbers, and the median is the middle of a set of numbers. Your text book should cover these concepts and how to calculate them at the very beginning. You can also find instructions at on websites like MathWorld. To calculate the mean, add all of the numbers in your data set and divide the sum by the number of numbers in the set. For example, if your data set includes the numbers 2, 4, 6, 8, 10, and 12, the sum of the set is 42. 42 divided by 6 (the number of data points) is 7. 7 is your mean. The median is the just the middle of any set of numbers. So the median of the data set 2, 4, 6, 8, and 10 is 6. If you have an even number of data points, add the 2 middle numbers of divide by 2. Once you know how to calculate mean, you can move on to more complicated concepts. Variance is the average of squared differences from the mean. Knowing the variance can help you understand how spread out a set of data is. For example, let's say you and your 3 friends each have a dog, and their heights are 12in (30cm), 20in (51cm), 16in (41cm), and 32in (81cm). First, take the mean of their heights by adding all 4 heights together and dividing by 4. In inches, this would be 12 + 20 + 16 + 32, which equals 80. Divide that by 4 (the total number of dogs) to get 20. So the mean of their heights is 20in (51cm). Then calculate the variance by subtracting each individual height from the mean and squaring it. So 20 - 12 is 8, and 8 squared is 64. 20 - 20 is 0, and 0 squared is still 0. 20 - 16 is 4, and 4 squared is 16. And 20 minus 32 is -12, and -12 squared is 144. 8 + 0 + 16 + 144 = 168. To get the final variance, divide the sum of the squared differences from the mean (168) by the number of dogs (4). So the variance of this data set is 42. Standard deviation tells you how much each data point differs from the mean. To calculate the standard deviation, you'll need the variance first. Then take the square root of the variance. If the resulting number includes a decimal (most will), round it to the nearest whole number. For example, if the variance of your and your friends' dogs' heights is 42, the standard deviation is the square root of 6.48. You'd round that down to 6. That tells you that, on average, each dog is about 6in (15cm) away from the mean of the dogs' heights. The normal distribution is a graphic distribution of a set of data's mean and the variations from the mean. You can learn a lot about a data set from normal distribution graphs. To learn how to calculate them, you'll need to calculate z values individual points on the graph. A table of z-values can usually be found in your text book. Your textbook should have detailed instructions on how to calculate points on a normal distribution graph. You can also find resources online, at websites like minitab or MathWorld.
Start with mean and median. Learn the connection between variance and mean. Understand the connection between variance and standard deviation. Learn to calculate normal distribution.