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It's going to have a mean right over here of, so this is the mean of our sampling distribution. So this is going to be equal to the same thing as our population proportion, 0.15. And we also know that our standard deviation here is going to be approximately equal to 0.028. And what we wanna know is what is the approxim... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
And what we wanna know is what is the approximate probability that more than 10% of the sample would report that they experienced extreme levels of stress during the past month? So we could say that 10% would be right over here. I'll say 0.10. And so the probability that in a sample of 160, you get a proportion for tha... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
And so the probability that in a sample of 160, you get a proportion for that sample, a sample proportion that is larger than 10% would be this area right over here. So this right over here would be the probability that your sample proportion is greater than, they say is more than 10%, is more than 0.1. I could write o... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
And then to calculate it, I can get out our calculator again. So here I'm gonna go to my distribution menu right over there. And then I'm gonna do a normal cumulative distribution function. So let me click Enter there. And so what is my lower bound? Well, my lower bound is 10%, 0.1. What is my upper bound? | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
So let me click Enter there. And so what is my lower bound? Well, my lower bound is 10%, 0.1. What is my upper bound? Well, we'll just make this one because that is the highest proportion you could have for a sampling distribution of sample proportions. Now what is our mean? Well, we already know that's 0.15. | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
What is my upper bound? Well, we'll just make this one because that is the highest proportion you could have for a sampling distribution of sample proportions. Now what is our mean? Well, we already know that's 0.15. What is the standard deviation of our sampling distribution? Well, it's approximately 0.028. And then I... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
Well, we already know that's 0.15. What is the standard deviation of our sampling distribution? Well, it's approximately 0.028. And then I can click Enter. And if you're taking an AP exam, you actually should write this. You should say, you should tell the graders what you're actually typing in in your normal CDF funct... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
And then I can click Enter. And if you're taking an AP exam, you actually should write this. You should say, you should tell the graders what you're actually typing in in your normal CDF function. But if we click Enter right over here, and then Enter, there we have it. It's approximately 96%. So this is approximately 0... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
But if we click Enter right over here, and then Enter, there we have it. It's approximately 96%. So this is approximately 0.96. And then out of our choices, it would be this one right over here. If you're taking this on the AP exam, you would say that called, called normal, normal CDF, where you have your lower bound, ... | Probability of sample proportions example Sampling distributions AP Statistics Khan Academy.mp3 |
At the end of each month, he obtains data from a random sample of adults on whether or not they currently approve of the prime minister's performance, using a separate sample each month. Derek wants to test if the proportion of adults who approved was significantly lower in December than it was in November. Which of th... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
Pause this video and see if you can figure it out on your own. All right, so let's think about ways to write a null hypothesis first. So remember, your null hypothesis is assuming that there's no news here, there's no difference. So one way to say it is that the true proportion in December is equal to your true proport... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
So one way to say it is that the true proportion in December is equal to your true proportion in November. Another way to write that exact same thing is to say that the difference between the true proportion in December, and let's see, they say Derek wants to test if the proportion of adults who approved was significan... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
So another way to say this exact same thing is that the true proportion in November minus the true proportion in December is equal to zero. So each of these would be legitimate null hypotheses. And so let's see, this one looks good, this one looks good, this one looks good. This one is not a legitimate null hypothesis ... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
This one is not a legitimate null hypothesis for what we're trying to do, so we could rule out D. And then the other one is this, Derek wants to test if the proportion of adults who approved was significantly lower in December than it was in November. So the news here would be, if this actually is the case, if we have ... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
Or it could be that the proportion in November is greater than the proportion in December. And if we look at these choices, the proportion in December is less than the proportion in November, that's what I wrote right over here, so that looks good as well. Here they swapped it, here they're saying our alternative hypot... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
Here they're just saying that we actually have a difference in proportions. And many times you will see something like this, but here Derek wants to test if the proportion of adults who approved was significantly lower in December than in November. He's not interested in the other way around. If it said Derek wants to ... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
If it said Derek wants to test if the proportion of adults who approved was significantly different in December than November, then you would pick choice C instead of choice A. But given the way it was phrased, I would pick choice A. Let's do another example. Here it says that Kylie has a dime and a nickel, and she won... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
Here it says that Kylie has a dime and a nickel, and she wonders if they have the same likelihood of showing heads when they are flipped. She flips each coin 100 times to test if there is a significant difference in the proportion of flips that they each land showing heads, which of the following is an appropriate set ... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
Try to do it on your own. All right, well, your null hypothesis would be that there is no difference, so that the proportion of getting heads with your dime is the same as the proportion of heads with your nickel. And then your alternative hypothesis, so it says here she wants to test if there is a significant differen... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
She's not trying to say if the proportion of dimes coming up head is significantly lower or significantly larger. She just cares about the difference, if there's a significant difference in the proportion of flips. So her alternative hypothesis is that there is a difference, that these two proportions are not equal to ... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
And so if we look at the choices, so this null hypothesis looks good. This null hypothesis does not look good. Remember, your null hypothesis, you're trying to assume that, man, there's no news here. So all of these null hypotheses, these A, B, and D's null hypotheses look good. And then the alternative hypothesis, thi... | Constructing hypotheses for two proportions AP Statistics Khan Academy.mp3 |
He noticed a positive linear relationship between the times on each task. Here is computer output on the sample data. So we have some statistics calculated on the reaction time, on the memory time, and then he had his computer do a regression for the data that he collected, and then we're told assume that all condition... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
So pause this video and have a go at it. All right, so let's just make sure we understand what is going on. So let's first think about the population. So I'll do that right over here. So in the population, there might be some true linear relationship. So in theory, on our x-axis, we would have our reaction time, and on... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
So I'll do that right over here. So in the population, there might be some true linear relationship. So in theory, on our x-axis, we would have our reaction time, and on our y-axis, you have your memory time. If you were able to plot every single possible data point, it might even be an infinite or near infinite, so it... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
If you were able to plot every single possible data point, it might even be an infinite or near infinite, so it would be very hard to do it, but if there was just some truth in the universe that says, yes, there actually is a positive linear relationship, and it looks like this, and you could describe that regression l... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
You input those data points into a computer, and it does a regression line, and it's trying to minimize the squared distance to all of these points, and so let's say it gets a regression line that looks something like this, where this regression line can be described as some estimate of the true y-intercept, so this wo... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
A is equal to this, the constant coefficient, and then the reaction coefficient, this is just telling us, hey, for every incremental change in the reaction, how much would we expect the memory time to change, or for every change in x, how much would we expect for a change in y, so this is actually our estimate of the s... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
Now, the problem is is that we don't know exactly what the standard deviation of the sampling distribution is, but we can estimate it. We can calculate the slope that we got for our sample regression line, minus the slope we're assuming in our null hypothesis, which is going to be equal to zero, so we know what we're a... | Calculating t statistic for slope of regression line AP Statistics Khan Academy.mp3 |
What I want to do in this video is review much of what we've already talked about and then hopefully build some of the intuition on why we divide by n minus 1 if we want to have an unbiased estimate of the population variance when we're calculating the sample variance. So let's think about a population. So let's say th... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So a sample of that population and at its size we have lowercase n data points. So let's think about all of the parameters and statistics that we know about so far. So the first is the idea of the mean. So if we're trying to calculate the mean for the population, is that going to be a parameter or a statistic? Well, wh... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So if we're trying to calculate the mean for the population, is that going to be a parameter or a statistic? Well, when we're trying to calculate it on the population, we are calculating a parameter. So let me write this down. So this is going to be, so for the population, we are calculating a parameter. And when we at... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So this is going to be, so for the population, we are calculating a parameter. And when we attempt to calculate something for a sample, we would call that a statistic. So how do we think about the mean for a population? Well, first of all, we denote it with the Greek letter mu. And we essentially take every data point ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
Well, first of all, we denote it with the Greek letter mu. And we essentially take every data point in our population. So we take the sum of every data point. So we start at the first data point and we go all the way to the capital Nth data point. So every data point we add up. So this is the ith data point. So X sub 1... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So we start at the first data point and we go all the way to the capital Nth data point. So every data point we add up. So this is the ith data point. So X sub 1 plus X sub 2 all the way to X sub capital N. And then we divide by the total number of data points we have. Well, how do we calculate the sample mean? Well, t... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So X sub 1 plus X sub 2 all the way to X sub capital N. And then we divide by the total number of data points we have. Well, how do we calculate the sample mean? Well, the sample mean, we do a very similar thing with the sample. And we denote it with an X with a bar over it. And that's going to be taking every data poi... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
And we denote it with an X with a bar over it. And that's going to be taking every data point in the sample, so going up to lowercase n, adding them up. So these are the sum of all the data points in our sample. And then dividing by the number of data points that we actually had. Now, the other thing that we're trying ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
And then dividing by the number of data points that we actually had. Now, the other thing that we're trying to calculate for the population, which was a parameter, and then we'll also try to calculate it for the sample and estimate it for the population, was the variance, which was a measure of how dispersed or how muc... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
And how do we denote and calculate variance for a population? Well, for a population, we'd say that the variance, we use the Greek letter sigma squared, is equal to, and you could view it as the mean of the squared distances from the population mean. But what we do is we take, for each data point, so I equal 1 all the ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So if you want to calculate this, you'd want to figure this out. Or that's one way to do it. We'll see there's other ways to do it, where you can kind of calculate them at the same time. But you would, the easiest or the most intuitive, calculate this first. And for each of the data points, take the data point and subt... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
But you would, the easiest or the most intuitive, calculate this first. And for each of the data points, take the data point and subtract it from that. Subtract the mean from that. Square it. And then divide by the total number of data points you have. Now we get to the interesting part, sample variance. There are seve... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
Square it. And then divide by the total number of data points you have. Now we get to the interesting part, sample variance. There are several ways where, when people talk about sample variance, there are several, I guess, tools in their toolkits, or there are several ways to calculate it. One way is the biased sample ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
There are several ways where, when people talk about sample variance, there are several, I guess, tools in their toolkits, or there are several ways to calculate it. One way is the biased sample variance, the non-unbiased estimator of the population variance. And that's denoted, usually denoted, by S with a subscript N... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
How would we calculate it? Well, we would calculate it very similar to how we calculated the variance right over here, but we would do it for our sample, not our population. So for every data point in our sample, so we have N of them, we take that data point and from it we subtract our sample mean, we subtract our samp... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
But we already talked about in the last video, how would we find what is our best unbiased estimate of the population variance? This is usually what we're trying to get at. We're trying to find an unbiased estimate of the population variance. Well, in the last video we talked about that if we want to have an unbiased e... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
Well, in the last video we talked about that if we want to have an unbiased estimate, and here in this video I want to give you a sense of the intuition why, we would take the sum, so we're going to go through every data point in our sample, we're going to take that data point, subtract from it the sample mean, square ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So this is going to be larger, this is going to be larger, this is going to be smaller. And this one we refer to the unbiased estimate. And this one we refer to the biased estimate. If people just write this, they're talking about the sample variance, it's a good idea to clarify which one they're talking about, but if ... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
If people just write this, they're talking about the sample variance, it's a good idea to clarify which one they're talking about, but if you had to guess and people give you no further information, they're probably talking about the unbiased estimate of the variance. So you'd probably divide by N minus 1. But let's th... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So let's imagine all of the data in a population, and I'm just going to plot them on a number line. All the data. So this is my number line, this is my number line, and let me plot all of the data points in my population. So this is some data, this is some data, here's some data, and here is some data here, and I can j... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So this is some data, this is some data, here's some data, and here is some data here, and I can just do as many points as I want. So these are just points on the number line. Now let's say I take a sample of this. So this is my entire population. So let's see how many I have. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So this is my entire population. So let's see how many I have. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. So in this case, what would be my big N? My big N would be 14. Now let's say I take a sample, a lowercase N of, let's say my sample size is 3. I could take, well, before I even think about that, let's think abo... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So in this case, what would be my big N? My big N would be 14. Now let's say I take a sample, a lowercase N of, let's say my sample size is 3. I could take, well, before I even think about that, let's think about roughly where the mean of this population would sit. So the way I drew it, and I'm not going to calculate i... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
I could take, well, before I even think about that, let's think about roughly where the mean of this population would sit. So the way I drew it, and I'm not going to calculate it exactly, it looks like the mean might sit someplace roughly right over here. So the mean, the true population mean, the parameter is going to... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
Now let's think about what happens when we sample. And I'm going to do just a very small sample size just to give us the intuition, but this is true of any sample size. So let's say we have sample size of 3. So there is some possibility when we take our sample size of 3 that we happen to sample it in a way that our sam... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So there is some possibility when we take our sample size of 3 that we happen to sample it in a way that our sample mean is pretty close to our population mean. So for example, if we sample to that point, that point, and that point, I could imagine our sample mean might actually sit pretty close to our population mean.... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
And the key idea here is when you take a sample, your sample mean is always going to sit within your sample. And so there is a possibility that when you take your sample, your mean could even be outside of the sample. And so in this situation, and this is just to give you an intuition, so here your sample mean is going... | Review and intuition why we divide by n-1 for the unbiased sample Khan Academy.mp3 |
So I have two different random variables here, and what I want to do is think about what type of random variables they are. So this first random variable, x, it's equal to the number of sixes after 12 rolls of a fair die. Well, this looks pretty much like a binomial random variable. In fact, I'm pretty confident it is ... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
In fact, I'm pretty confident it is a binomial random variable, and we could just go down the checklist. The outcome of each trial can be a success or failure. So trial, outcome, success, or failure. It's either gonna go either way. The result of each trial is independent from the other ones. Whether I get a six on the... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
It's either gonna go either way. The result of each trial is independent from the other ones. Whether I get a six on the third trial is independent on whether I got a six on the first or the second trial. So result, let me write this trial, I'll just do a shorthand trial, results, results, independent. Independent, tha... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
So result, let me write this trial, I'll just do a shorthand trial, results, results, independent. Independent, that's an important condition. Let's see, there are a fixed number of trials, fixed number of trials. In this case, we're gonna have 12 trials. And then the last one is we have the same probability on each tr... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
In this case, we're gonna have 12 trials. And then the last one is we have the same probability on each trial. Same probability of success. Probability on each trial. So yes, indeed, this met all the conditions for being a binomial, binomial random, random variable. And this was all just a little bit of review about th... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
Probability on each trial. So yes, indeed, this met all the conditions for being a binomial, binomial random, random variable. And this was all just a little bit of review about things that we have talked about in other videos. But what about this thing in the salmon color, the random variable Y? So this says the numbe... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
But what about this thing in the salmon color, the random variable Y? So this says the number of rolls until we get a six on a fair die. So this one strikes us as a little bit different, but let's see where it is actually different. So does it meet that the trial outcomes, that there's a clear success or failure for ea... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
So does it meet that the trial outcomes, that there's a clear success or failure for each trial? Well, yeah, we're just gonna keep rolling. So each time we roll, it's a trial. And success is when we get a six, failure is when we don't get a six. So the outcome of each trial can be classified as either a success or fail... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
And success is when we get a six, failure is when we don't get a six. So the outcome of each trial can be classified as either a success or failure. So it meets, and let me put the checks right over here, it meets this first constraint. Are the results of each trial independent? Well, whether I get a six on the first r... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
Are the results of each trial independent? Well, whether I get a six on the first roll or the second roll or the third roll or the fourth roll or the third roll, the probabilities shouldn't be dependent on whether I did or didn't get a six on a previous roll. So we have the independence. And we also have the same proba... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
And we also have the same probability of success on each trial. In every case, it's a 1 6th probability that I get a six. So this stays constant. And I skipped this third condition for a reason. Because we clearly don't have a fixed number of trials. Over here, we could roll 50 times until we get a six. The probability... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
And I skipped this third condition for a reason. Because we clearly don't have a fixed number of trials. Over here, we could roll 50 times until we get a six. The probability that we'd have to roll 50 times is very low, but we might have to roll 500 times in order to get a six. In fact, think about what the minimum val... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
The probability that we'd have to roll 50 times is very low, but we might have to roll 500 times in order to get a six. In fact, think about what the minimum value of y is and what the maximum value of y is. So the minimum value that this random variable can take, I'll just call it min y, is equal to what? Well, it's g... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
Well, it's gonna take at least one roll, so that's the minimum value. But what is the maximum value for y? And I'll let you think about that. Well, I've assumed you've thought about it if you paused the video. Well, there is no max value. You can't say, oh, it's a billion, because there's some probability that it might... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
Well, I've assumed you've thought about it if you paused the video. Well, there is no max value. You can't say, oh, it's a billion, because there's some probability that it might take a billion and one rolls. That is a very, very, very, very, very, very small probability, but there's some probability it could take a Go... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
That is a very, very, very, very, very, very small probability, but there's some probability it could take a Google rolls, a Googleplex rolls, so you can imagine where this is going. So this type of random variable, where it meets a lot of the constraints of a binomial random variable, each trial has a clear success or... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
Maybe that's a general way of framing this type of random variable. How many trials until success, while the binomial random variable was, how many trials, or how many successes, I should say, how many successes in finite number of trials? So if you see this general form and it meets these conditions, you can feel good... | Geometric random variables introduction Random variables AP Statistics Khan Academy.mp3 |
And what I'm going to ask you is, which of these intervals, interval A, B, or C, which one contains the median of the scores, and which one, or give an estimate of which one contains the mean of the scores? Pause this video and see if you can figure that out. So let's just start with the median. Remember, the median yo... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
Remember, the median you could view as the middle number, or if you have an even number of data points, it would be the average of the middle two. Here we have an odd number of data points, so it would be the middle number. So what would be the middle number if you were to order them from least to greatest? Well, it wo... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
Well, it would be the one that has 15 on either side, so it would be the 16th data point. 16th data point. And so we could just think about which interval here contains the 16th data point. You could view it for the 16th from the highest, or the 16th from the lowest. It is the middle one. All right, so let's start from... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
You could view it for the 16th from the highest, or the 16th from the lowest. It is the middle one. All right, so let's start from the highest. So this interval C contains the 13 highest data points, and then interval B goes from the 14th highest all the way to the 18th highest. So this B contains the median. It contai... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
So this interval C contains the 13 highest data points, and then interval B goes from the 14th highest all the way to the 18th highest. So this B contains the median. It contains the 16th highest data point, or if you started from the left, it would also be the 16th lowest data point. So that's where the median is, the... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
So that's where the median is, the median. Now what about an estimate for the mean? Well, you have calculated the mean in the past, but when you're looking at a distribution like this, when you're looking at a histogram, one way to think about the mean is it would be the balancing point. If you imagine that this histog... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
If you imagine that this histogram was made out of some material of, let's say, uniform density, where would you put a fulcrum in order to balance it? If you put the fulcrum right over here, it feels like you would have, it feels like you would tip over to the left because this is a left-skewed distribution. You have t... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
If you really wanted to balance it out, it seems like you would have to move your fulcrum in the direction of that left skew, in the direction of the tail. And so I would estimate to balance it out, it would actually be closer to that, which would be interval A. Interval A would contain the mean. The intention of this ... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
In fact, they don't give you all the information here and add them all up and then divide by 31. It's really to estimate and to also get the intuition that when you have a left-skewed distribution like this, you will often see a situation where your mean is to the left of the median. If you have a right-skewed distribu... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
And as we will see, when you see a symmetric distribution, the mean and the median will be awfully close to each other or when you have a roughly symmetric distribution. If you have a perfectly symmetric distribution, they might be exactly in the same place. So let's do another example. So here it says we have the ages... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
So here it says we have the ages of 14 coworkers and what I want you to do is say roughly where is the mean and roughly where is the median? Is it roughly at A, is it roughly at B, or is it roughly at C? Pause this video and try to figure it out. So let's first start off with the median. We have 14 data points. So this... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
So let's first start off with the median. We have 14 data points. So this would be the average of the middle two data points. It would be the average of the seventh and eighth data point. Well, you could say one, two, three, four, five, six, seven, and then the eighth one is here. So the seventh data point is a 30. The... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
It would be the average of the seventh and eighth data point. Well, you could say one, two, three, four, five, six, seven, and then the eighth one is here. So the seventh data point is a 30. The eighth one is in the 31 bucket. So the average of the two would get you to B. Another way that you could think about it is yo... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
The eighth one is in the 31 bucket. So the average of the two would get you to B. Another way that you could think about it is you can just eyeball it and see you have just as many data points below B as you do have above B and so that also gives you a good indication that B would be where the median is. So that is whe... | Estimating mean and median in data displays AP Statistics Khan Academy.mp3 |
Let's say that you have a cherry pie store, and you've noticed that there is variability in the number of cherries on each pie that you sell. Some pies might have over 100 cherries, while other pies might have fewer than 50 cherries. So what you're curious about is what is the distribution? How many of the different ty... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
How many of the different types of pies do you have? How many pies do you have that have a lot of cherries? How many pies do you have that have very few cherries? How many pies are in between? And so to do that, you set up a histogram. What you do is you take each pie in your store. Let's see if I can draw a pie of som... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
How many pies are in between? And so to do that, you set up a histogram. What you do is you take each pie in your store. Let's see if I can draw a pie of some kind. It's a cherry pie. I don't know if this is an adequate drawing of a pie. But you take each of the pies in your store, and you count the number of cherries ... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
Let's see if I can draw a pie of some kind. It's a cherry pie. I don't know if this is an adequate drawing of a pie. But you take each of the pies in your store, and you count the number of cherries on it. So this pie right over here is one, two, three, four, five, six, seven, eight, nine, ten. Let's see, you keep coun... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
But you take each of the pies in your store, and you count the number of cherries on it. So this pie right over here is one, two, three, four, five, six, seven, eight, nine, ten. Let's see, you keep counting, and let's say it has 32 cherries. And you do that for every pie. And then you created buckets, because you don'... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
And you do that for every pie. And then you created buckets, because you don't want to create just a graph of how many have exactly 32. You just want to get a general sense of things. So you create buckets of 30. You say, how many pies have between zero and 29 cherries? How many pies have between 30 and 59, including 3... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
So you create buckets of 30. You say, how many pies have between zero and 29 cherries? How many pies have between 30 and 59, including 30 and 59? How many pies have at least 60 and at most 89 cherries? How many pies have at least 90 and at most 119? And then how many pies have at least 120 and at most 149? And you know... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
How many pies have at least 60 and at most 89 cherries? How many pies have at least 90 and at most 119? And then how many pies have at least 120 and at most 149? And you know that you don't have any pies that have more than 149 cherries. So this should account for everything. And then you count them. So for example, yo... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
And you know that you don't have any pies that have more than 149 cherries. So this should account for everything. And then you count them. So for example, you say, okay, five pies have 30 to 59 cherries. And so we create a histogram, or you create a histogram, and you make this magenta bar go up to five. So that's how... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
So for example, you say, okay, five pies have 30 to 59 cherries. And so we create a histogram, or you create a histogram, and you make this magenta bar go up to five. So that's how you would construct this histogram. That's what this pies at different cherry levels histogram is telling us. So now that we know how to co... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
That's what this pies at different cherry levels histogram is telling us. So now that we know how to construct it, let's see if we can interpret it based on the information given in the histogram. So the first question is, based on just this information, can you figure out the total number of pies in your store, assumi... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
And I encourage you to pause the video and try to figure it out on your own. Well, what's the total number of pies? Well, let's see. There's five pies that have more than, or 30 or more, have at least 30 cherries, but no more than 59. You have eight pies in this blue bucket. You have four pies in this green bucket. And... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
There's five pies that have more than, or 30 or more, have at least 30 cherries, but no more than 59. You have eight pies in this blue bucket. You have four pies in this green bucket. And then you have, what is this, five, no, this is three pies that have at least 120, but no more than 149 cherries. And this accounts f... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
And then you have, what is this, five, no, this is three pies that have at least 120, but no more than 149 cherries. And this accounts for all of the pies. So the total number of pies you have at this store are five plus eight plus four plus three, which is what? Five plus eight is 13, plus four is 17, plus three is 20... | How to interpret a histogram Data and statistics 6th grade Khan Academy.mp3 |
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