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The expected value of negative Y, I'll do it over here, the expected value of the negative of a random variable is just the negative of the expected value of that random variable. So if you look at this, we can rewrite this. I'll give myself a little bit more space. We can rewrite this as the expected value, the varian... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
We can rewrite this as the expected value, the variance of negative Y is the expected value. This is just 1. Negative 1 squared is just 1. And over here you have Y. And instead of just writing plus the expected value of negative Y, that's the same thing as minus the expected value of Y. So you have that and then all of... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
And over here you have Y. And instead of just writing plus the expected value of negative Y, that's the same thing as minus the expected value of Y. So you have that and then all of that squared. Now notice, this is the exact same thing by definition as the variance of Y. So we just showed you just now, so this is the ... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
Now notice, this is the exact same thing by definition as the variance of Y. So we just showed you just now, so this is the variance of Y. So we just showed you that the variance of the difference of two independent random variables is equal to the sum of the variances. You could definitely believe this. It's equal to ... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
You could definitely believe this. It's equal to the sum of the variance of the first one plus the variance of the negative of the second one. And we just showed that that variance is the same thing as the variance of the positive version of that variable, which makes sense. Your distance from the mean is going to be, ... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
Your distance from the mean is going to be, it doesn't matter whether you're taking the positive or the negative of the variable. You just care about absolute distance. So it makes complete sense that that quantity and that quantity is going to be the same thing. So the whole reason why I went through this exercise, th... | Variance of differences of random variables Probability and Statistics Khan Academy.mp3 |
A cereal company is giving away a prize in each box of cereal, and they advertise, collect all six prizes. Each box of cereal has one prize, and each prize is equally likely to appear in any given box. Amanda wonders how many boxes it takes, on average, to get all six prizes. So there's several ways to approach this fo... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So there's several ways to approach this for Amanda. She could try to figure out a mathematical way to determine what is the expected number of boxes she would need to collect, on average, to get all six prizes. Or she could run some random numbers to simulate collecting box after box after box and figure out multiple ... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So for example, she could say, alright, each box is gonna have one of six prizes. So there could be, she could assign a number for each of the prizes, one, two, three, four, five, six. And then she could have a computer generate a random string of numbers, maybe something that looks like this. And the general method, s... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
And the general method, she could start at the left here, and each new number she gets, she can say, hey, this is like getting a cereal box, and then it's going to tell me which prize I got. So she starts her first experiment, she'll start here at the left, and she'll say, okay, the first cereal box of this experiment,... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
You might say, well look, there are numbers here that aren't one through six. There's zero, there's seven, there's eight or nine. Well, for those numbers, she could just ignore them. She could just pretend like they aren't there, and just keep going past them. So why don't you pause this video, and do it for the first ... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
She could just pretend like they aren't there, and just keep going past them. So why don't you pause this video, and do it for the first experiment. On this first experiment, using these numbers, assuming that this is the first box that you are getting in your simulation, how many boxes would you need in order to get a... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So let's, let me make a table here. So this is the experiment. And then in the second column, I'm gonna say number of boxes. Number of boxes you would have to get in that simulation. So maybe I'll do the first one in this blue color. So we're in the first simulation. So one box, we got the one. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Number of boxes you would have to get in that simulation. So maybe I'll do the first one in this blue color. So we're in the first simulation. So one box, we got the one. Actually, maybe I'll check things off. So we have to get a one, a two, a three, a four, a five, and a six. So let's see, we have a one. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So one box, we got the one. Actually, maybe I'll check things off. So we have to get a one, a two, a three, a four, a five, and a six. So let's see, we have a one. I'll check that off. We have a five. I'll check that off. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So let's see, we have a one. I'll check that off. We have a five. I'll check that off. We get a six. I'll check that off. Well, the next box, we got another six. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
I'll check that off. We get a six. I'll check that off. Well, the next box, we got another six. We've already have that prize, but we're gonna keep getting boxes. Then the next box, we get a two. Then the next box, we get a four. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Well, the next box, we got another six. We've already have that prize, but we're gonna keep getting boxes. Then the next box, we get a two. Then the next box, we get a four. Then the next box, the number's a seven. So we will just ignore this right over here. The box after that, we get a six, but we already have that p... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Then the next box, we get a four. Then the next box, the number's a seven. So we will just ignore this right over here. The box after that, we get a six, but we already have that prize. Then we ignore the next box, a zero. That doesn't give us a prize. We assume that that didn't even happen. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
The box after that, we get a six, but we already have that prize. Then we ignore the next box, a zero. That doesn't give us a prize. We assume that that didn't even happen. And then we would go to the number three, which is the last prize that we need. So how many boxes did we have to go through? Well, we would only co... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
We assume that that didn't even happen. And then we would go to the number three, which is the last prize that we need. So how many boxes did we have to go through? Well, we would only count the valid ones, the ones that gave a valid prize between the numbers one through six, including one and six. So let's see. We wen... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Well, we would only count the valid ones, the ones that gave a valid prize between the numbers one through six, including one and six. So let's see. We went through one, two, three, four, five, six, seven, eight boxes in the first experiment. So experiment number one, it took us eight boxes to get all six prizes. Let's... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So experiment number one, it took us eight boxes to get all six prizes. Let's do another experiment, because this doesn't tell us that, on average, she would expect eight boxes. This just meant that on this first experiment, it took eight boxes. If you wanted to figure out, on average, you wanna do many experiments. An... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
If you wanted to figure out, on average, you wanna do many experiments. And the more experiments you do, the better that that average is going to, the more likely that your average is going to predict what it actually takes, on average, to get all six prizes. So now let's do our second experiment. And remember, it's im... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
And remember, it's important that these are truly random numbers. And so we will now start at the first valid number. So we have a two. So this is our second experiment. We got a two. We got a one. We can ignore this eight. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So this is our second experiment. We got a two. We got a one. We can ignore this eight. Then we get a two again. We already have that prize. Ignore the nine. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
We can ignore this eight. Then we get a two again. We already have that prize. Ignore the nine. Five, that's a prize we need in this experiment. Nine, we can ignore. And then four, haven't gotten that prize yet in this experiment. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Ignore the nine. Five, that's a prize we need in this experiment. Nine, we can ignore. And then four, haven't gotten that prize yet in this experiment. Three, haven't gotten that prize yet in this experiment. One, we already got that prize. Three, we already got that prize. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
And then four, haven't gotten that prize yet in this experiment. Three, haven't gotten that prize yet in this experiment. One, we already got that prize. Three, we already got that prize. Three, already got that prize. Two, two, already got those prizes. Zero, we already got all of these prizes over here. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Three, we already got that prize. Three, already got that prize. Two, two, already got those prizes. Zero, we already got all of these prizes over here. We can ignore the zero. Already got that prize. And finally, we get prize number six. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Zero, we already got all of these prizes over here. We can ignore the zero. Already got that prize. And finally, we get prize number six. So how many boxes did we need in that second experiment? Well, let's see. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17 boxes. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
And finally, we get prize number six. So how many boxes did we need in that second experiment? Well, let's see. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17 boxes. So in experiment two, I needed 17, or Amanda needed 17 boxes. And she can keep going. Let's do this one more time. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17 boxes. So in experiment two, I needed 17, or Amanda needed 17 boxes. And she can keep going. Let's do this one more time. This is strangely fun. So experiment three. Now remember, we only wanna look at the valid numbers. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Let's do this one more time. This is strangely fun. So experiment three. Now remember, we only wanna look at the valid numbers. We'll ignore the invalid numbers, the ones that don't give us a valid prize number. So four, we get that prize. These are all invalid. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Now remember, we only wanna look at the valid numbers. We'll ignore the invalid numbers, the ones that don't give us a valid prize number. So four, we get that prize. These are all invalid. In fact, and then we go to five, we get that prize. Five, we already have it. We get the two prize. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
These are all invalid. In fact, and then we go to five, we get that prize. Five, we already have it. We get the two prize. Seven and eight are invalid. Seven's invalid. Six, we get that prize. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
We get the two prize. Seven and eight are invalid. Seven's invalid. Six, we get that prize. Seven's invalid. One, we got that prize. One, we already got it. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Six, we get that prize. Seven's invalid. One, we got that prize. One, we already got it. Nine's invalid. Two, we already got it. Nine is invalid. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
One, we already got it. Nine's invalid. Two, we already got it. Nine is invalid. One, we already got the one prize. And then finally, we get prize number three, which was the missing prize. So how many boxes, valid boxes, did we have to go through? | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Nine is invalid. One, we already got the one prize. And then finally, we get prize number three, which was the missing prize. So how many boxes, valid boxes, did we have to go through? Let's see. One, two, three, four, five, six, seven, eight, nine, 10. 10. | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
So how many boxes, valid boxes, did we have to go through? Let's see. One, two, three, four, five, six, seven, eight, nine, 10. 10. So with only three experiments, what was our average? Well, with these three experiments, our average is going to be eight plus 17 plus 10 over three. So let's see, this is 2535 over three... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
10. So with only three experiments, what was our average? Well, with these three experiments, our average is going to be eight plus 17 plus 10 over three. So let's see, this is 2535 over three, which is equal to 11 2 3rds. Now, do we know that this is the true theoretical expected number of boxes that you would need to... | Random number list to run experiment Probability AP Statistics Khan Academy.mp3 |
Estella oversees 12 of these residence halls. Her department surveyed a large, simple, random sample of first-year students who live in those 12 residence halls about their overall satisfaction with campus living. Estella can safely generalize the results of the survey to which population. So pause this video and see i... | Generalizabilty of survey results example Study design AP Statistics Khan Academy.mp3 |
So pause this video and see if you can figure it out. Alright, so let's do this together. So Estella has done, it's a large, simple, random sample of first-year students. So let's see. Choice A is only those students who were surveyed. Well no, this was a simple, random sample and it was a large sample, so it's meant t... | Generalizabilty of survey results example Study design AP Statistics Khan Academy.mp3 |
So let's see. Choice A is only those students who were surveyed. Well no, this was a simple, random sample and it was a large sample, so it's meant to be indicative of all first-year students. You can generalize more than just making statements about just the students who were surveyed. All first-year students, but onl... | Generalizabilty of survey results example Study design AP Statistics Khan Academy.mp3 |
You can generalize more than just making statements about just the students who were surveyed. All first-year students, but only those who live in these 12 residence halls. Yeah, I think this one looks fair, because you can't generalize to people who don't live in those residence halls. Maybe Estella oversees the 12 be... | Generalizabilty of survey results example Study design AP Statistics Khan Academy.mp3 |
Maybe Estella oversees the 12 best residence halls or the 12 worst residence halls. And so you wouldn't get, if that were the case, you would not be able to generalize beyond that. Or these might be the 12 that are closest to campus or the 12 that are furthest from campus. So you can only generalize to people who live ... | Generalizabilty of survey results example Study design AP Statistics Khan Academy.mp3 |
A statistician for a basketball team tracked the number of points that each of the 12 players on the team had in one game, and then made a stem and the leaf plot to show the data. Sometimes it's called a stem plot. How many points did the team score? And when you first look at this plot right over here, it seems a litt... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And when you first look at this plot right over here, it seems a little hard to understand. Under stem you have zero, one, two. Under leaf you have all of these digits here. How does this relate to the number of points each student or each player actually scored? And the way to interpret a stem and leaf plot is the lea... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
How does this relate to the number of points each student or each player actually scored? And the way to interpret a stem and leaf plot is the leaf contain, at least the way that this statistician used it, the leaf contains the smallest digit, or the ones digit, in the number of points that each player scored, and the ... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And what's useful about this is it gives kind of a distribution of where the players were. You see that most of the players scored points that started with a zero, then a few more scored points that started with a one, and then only one score scored points that started with a two, and it was actually 20 points. So let ... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So I'm gonna write the zeros in purple. So there's, let's see, one, two, three, four, five, six, seven players had zero as the first digit. So one, two, three, four, five, six, seven. I wrote seven zeros, and then this player also had a zero in his ones digit. This player, I'm gonna try to do all the colors, this playe... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
I wrote seven zeros, and then this player also had a zero in his ones digit. This player, I'm gonna try to do all the colors, this player also had a zero in his ones digit. This player right here had a two in his ones digit, so he scored a total of two points. This player, let me do orange, this player had four for his... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
This player, let me do orange, this player had four for his ones digit. This player had seven for his ones digit. Then this player had seven for his ones digit. And then, let me see, I'm almost using all the colors, this player had nine for his ones digit. So the way to read this is you had one player with zero points,... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And then, let me see, I'm almost using all the colors, this player had nine for his ones digit. So the way to read this is you had one player with zero points, zero, two, four, seven, nine, and nine. But you can see, I'm just kind of silly saying the zero was the tens digit. You could have even put a blank there, but t... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
You could have even put a blank there, but the zero lets us know that they didn't score, they didn't score anything in the tens place. But these are the actual scores for those seven players. Now let's go to the next row in the stem and leaf plot. So over here, all of the digits start with, or all of the points start w... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So over here, all of the digits start with, or all of the points start with one for each of the players, and there's four of them. So one, one, one, and one. And then we have this player over here, it's one, his ones digit, or her ones digit is a one. So this player, this represents 11. One in the tens place, one in th... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So this player, this represents 11. One in the tens place, one in the ones place. This player over here also got 11. One in the tens place, one in the ones place. This player, let me do orange. This player has three in the ones place. So he or she scored 13 points. | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
One in the tens place, one in the ones place. This player, let me do orange. This player has three in the ones place. So he or she scored 13 points. One in the tens place, three in the ones place, 13 points. And then, I will do this in purple, this player has eight in their ones place. So he or she scored 18 points. | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So he or she scored 13 points. One in the tens place, three in the ones place, 13 points. And then, I will do this in purple, this player has eight in their ones place. So he or she scored 18 points. One in the tens place, eight in the ones place, 18 points. And then finally, you have this player that has two, the tens... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So he or she scored 18 points. One in the tens place, eight in the ones place, 18 points. And then finally, you have this player that has two, the tens digit is a two, and then the ones digit is a zero. Is a zero, I'll circle that in yellow. It is a zero. So he or she scored 20 points. So using, looking at the stem and... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Is a zero, I'll circle that in yellow. It is a zero. So he or she scored 20 points. So using, looking at the stem and leaf plot, we're able to extract out all of the number of points that all of the players scored. And once again, what was useful about this is you see how many players scored between zero and nine point... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So using, looking at the stem and leaf plot, we're able to extract out all of the number of points that all of the players scored. And once again, what was useful about this is you see how many players scored between zero and nine points, including nine points. How many scored between 10 and 19 points, and then how man... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And you see the distribution right over here. But let's actually answer the question that they're asking us to answer. How many points did the team score? So here, we just have to add up all of these numbers right over here. So we're going to add up, I'll start with the largest. So 20 plus 18 plus 13 plus 11 plus 11, 1... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
So here, we just have to add up all of these numbers right over here. So we're going to add up, I'll start with the largest. So 20 plus 18 plus 13 plus 11 plus 11, 13, 11, 11, plus nine plus seven, plus seven again, plus four, plus two. Did I do that right? We have two 11s, then a nine, then two sevens, then a four, th... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Did I do that right? We have two 11s, then a nine, then two sevens, then a four, then a two, and then these two characters didn't score anything. So let's add up all of these together. Let's add them all up. So zero plus eight is eight, plus three is 11, plus one is 12, plus one is 13, plus nine is 22, plus seven is 27... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Let's add them all up. So zero plus eight is eight, plus three is 11, plus one is 12, plus one is 13, plus nine is 22, plus seven is 27, 34, 38, 30, or 40. So that gets us to 40. Let me do that one more time. Eight, 11, 11, 12, 13, 22, 29, 29, and then, 29, 36, 40, and 42. Looks like I actually might have messed, let m... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Let me do that one more time. Eight, 11, 11, 12, 13, 22, 29, 29, and then, 29, 36, 40, and 42. Looks like I actually might have messed, let me do it one more time. This is the hardest part, adding these up. So let me try that one last time. I'm just going to state where my sum is. So zero, eight, add three, 11, 12, 13,... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
This is the hardest part, adding these up. So let me try that one last time. I'm just going to state where my sum is. So zero, eight, add three, 11, 12, 13, 22, 29, 36, 40, 42. So it's a good thing that I double-checked that, I made a mistake the first time. Four plus two is six, seven, eight, nine, 10. So we get to 10... | Stem-and-leaf plots Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And so we're gonna get an example of doing that right over here. Sometimes in life, say on an exam, especially on something like an AP exam, you're asked to describe or compare a distribution. And what we're going to do in this video is do exactly that. In fact, this one we're going to describe, and then in a future vi... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
In fact, this one we're going to describe, and then in a future video, we're going to compare distributions. Now before we even read about this distribution or look at this distribution, if you're asked to describe a distribution, there's four things that you should be thinking about. You should be thinking about the s... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
And when we're talking about shape, it's going to be, there could be left skew, there could be right skew, and we'll see examples of these. We've talked about them in detail in other videos. They could be symmetric. These are the ones that we typically see, although there might be other types of shapes. You will have y... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
These are the ones that we typically see, although there might be other types of shapes. You will have your center of distribution. And there's multiple ways of thinking about the center of distribution. We've talked about this before. You have your mean, you have your median. These are the two most typical ones. You h... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
We've talked about this before. You have your mean, you have your median. These are the two most typical ones. You have a notion of spread. And for spread, you could use range, you could use interquartile range, you could use something like a mean absolute deviation, you could use a, you could use the standard deviatio... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
You have a notion of spread. And for spread, you could use range, you could use interquartile range, you could use something like a mean absolute deviation, you could use a, you could use the standard deviation. These are all measures of spread. And then you probably should at least comment about outliers, even if you ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
And then you probably should at least comment about outliers, even if you don't see them. It's a good idea to comment, just to make sure that you are being relatively comprehensive. So now, given that, let's do, let's describe the distribution right over here. It says, in the state of Connecticut, the Department of Mot... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
It says, in the state of Connecticut, the Department of Motor Vehicles, the DMV, requires 16 and 17 year olds to take a 25 question knowledge test in order to obtain a learner's permit. To pass, prospective drivers must correctly answer at least 20 questions. On one Monday, 22 teenagers took the test. The dot plot belo... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
The dot plot below shows their scores. So why don't you pause this video and see if you can take a shot at describing the shape, the center, the spread, and the outliers. Some of these you might be able to come with the actual numbers. You might be able to calculate some of these. But really, just to get a sense of it,... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
You might be able to calculate some of these. But really, just to get a sense of it, why don't you take a shot at it? All right, now let's do this together. So first, on the shape. So what we see is we have, most of the distribution is in this part between 20 and 25. But then we have this fairly long tail to the left. ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
So first, on the shape. So what we see is we have, most of the distribution is in this part between 20 and 25. But then we have this fairly long tail to the left. And so this tells us that we have a left skew, or it is a left skewed distribution right over here. So we have done the shape. It's a left skewed distributio... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
And so this tells us that we have a left skew, or it is a left skewed distribution right over here. So we have done the shape. It's a left skewed distribution because the tail goes to the left. Now what about the center of this distribution? So there's a few ways to measure center, mean or median. Just for the sake of ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
Now what about the center of this distribution? So there's a few ways to measure center, mean or median. Just for the sake of simplicity, I'll think about the median here. I can eyeball that to some degree. You could also calculate the mean. It would take a little bit more time. I would guess that it's someplace, not e... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
I can eyeball that to some degree. You could also calculate the mean. It would take a little bit more time. I would guess that it's someplace, not even calculating it, I would guess that it's someplace in this range right over there. But let me actually calculate it. So the median, there's 22 data points. So the median... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
I would guess that it's someplace, not even calculating it, I would guess that it's someplace in this range right over there. But let me actually calculate it. So the median, there's 22 data points. So the median is whatever number has 11 on to the right of it and 11 to the left, half of 22. So let's see. We have one, ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
So the median is whatever number has 11 on to the right of it and 11 to the left, half of 22. So let's see. We have one, two, three, four, five, six, seven, eight, nine, 10, 11. So the median here is going to be, let's see, this is 23 because we have a bunch of 23s. One, two, three, four, five, six 23s. And if we were ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
So the median here is going to be, let's see, this is 23 because we have a bunch of 23s. One, two, three, four, five, six 23s. And if we were to just order all of the data points, 11 of the data points would be 23 or less, and then 11 would be 23 or more. So our median here, so I could say our center is 23 if we use th... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
So our median here, so I could say our center is 23 if we use the median. And actually, let me write that down. So our median is 23. That's the measure of center that I decided to use. Now, what about spread? Well, the simplest measure of spread is just the range, which is the highest value minus the lowest value. And ... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
That's the measure of center that I decided to use. Now, what about spread? Well, the simplest measure of spread is just the range, which is the highest value minus the lowest value. And so our range here would be 25 minus four. 25 minus four is equal to 21. So that is a measure of range. You could have others, but thi... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
And so our range here would be 25 minus four. 25 minus four is equal to 21. So that is a measure of range. You could have others, but this one is very easy to calculate. And then if we think about outliers, well, there are a few outliers I would consider, and it's very subjective. People can debate if there's a dot rig... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
You could have others, but this one is very easy to calculate. And then if we think about outliers, well, there are a few outliers I would consider, and it's very subjective. People can debate if there's a dot right over there, is that an outlier or not? But I would say that these four right over here, I would consider... | Example Describing a distribution AP Statistics Khan Academy.mp3 |
And if you don't know what antibodies are, these are things that your immune system keeps around so it's very easy to recognize future infection. But you don't have to worry too much about that for this video. In this video, we're just trying to think about how we can visualize data to understand if there's a relations... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
So let's say we go out and collect a bunch of data. So we test 120 adults and 114 have antibodies, six don't. We test 60 children, 54 have antibodies, six don't. We test 20 infants and then eight have antibodies and 12 don't. So we can just look at this data but this really still doesn't give us a visual representation... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
We test 20 infants and then eight have antibodies and 12 don't. So we can just look at this data but this really still doesn't give us a visual representation of what's going on. One step we can take, it still doesn't give us a fully visual representation, is to just think about percentages that might help us think abo... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
So if we calculate the percentages, we might see something like this. For example, 114 over 120 is 95% or 95% have antibodies. That 114 over 120 is 95%. And then the number that don't have antibodies, this six right over here, that is 5%, six over 120. And you can do that for each of the categories. 54 over 60 is 90% w... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
And then the number that don't have antibodies, this six right over here, that is 5%, six over 120. And you can do that for each of the categories. 54 over 60 is 90% while six over 60, you can do that math in your head, is 10%. And we could do the same thing for the infants. Eight out of 20 is 40% while 12 out of 20 is... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
And we could do the same thing for the infants. Eight out of 20 is 40% while 12 out of 20 is 60%. So that helps us a little bit. It helps us think about, well, what's the percentage of adults that have the antibody or children or infants? But if we really wanna visualize it, we can look at two different types of visual... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
It helps us think about, well, what's the percentage of adults that have the antibody or children or infants? But if we really wanna visualize it, we can look at two different types of visualizations. One, we can call a segmented bar chart. And I will show a segmented bar chart for this data right over here. Now in a s... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
And I will show a segmented bar chart for this data right over here. Now in a segmented bar chart, we group, we have a bar for each category here, and we're making adults, children, and infants the different categories, because we're thinking maybe that has something to do with the likelihood of having antibodies. And ... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
So 95% of the adult bar is filled in blue. That's for yes, they have the antibodies, and 5% is filled in red. And then for children, you can see that 90% is filled in blue and 10% is filled in red because 10% don't have the antibodies. And then for infants, you can see that 40% is filled in blue and 60% don't have the ... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
And then for infants, you can see that 40% is filled in blue and 60% don't have the antibodies. Now this by itself is pretty useful to visually see, all right, it looks like adults are much more likely to have the antibodies than children, and children are far more likely to have the antibodies than infants. And so it ... | Mosaic plots and segmented bar charts Exploring two-variable data AP Statistics Khan Academy.mp3 |
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