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And you see, when you look at many, many, many, many, many samples, something interesting is happening. When you look at the mean of those samples, when you average together those curves from all of those samples, you see that our best estimate is when a is pretty close to negative one, is when this is n plus negative ... | Simulation providing evidence that (n-1) gives us unbiased estimate Khan Academy.mp3 |
Anything less than negative one, so if we have n plus zero, if we divide by n, or if we have n plus.05, or whatever it might be, we start underestimating, we start underestimating the population variance. And you can do this for samples of different sizes. Let me try a sample size six. And here you go, once again, as I... | Simulation providing evidence that (n-1) gives us unbiased estimate Khan Academy.mp3 |
Assume the method of placing each cake order is independent. So C, if we assume a few things, is a classic geometric random variable. What tells us that? Well, the giveaway is that we're gonna keep doing these independent trials where the probability of success is constant and there's a clear success. A telephone order... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
Well, the giveaway is that we're gonna keep doing these independent trials where the probability of success is constant and there's a clear success. A telephone order in this case is a success. The probability is 10% of it happening. And we're gonna keep doing it until we get a success. So classic geometric random vari... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
And we're gonna keep doing it until we get a success. So classic geometric random variable. Now they ask us, find the probability, the probability that it takes fewer than five orders for Liliana to get her first telephone order of the month. So it's really the probability that C is less than five. So like always, paus... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
So it's really the probability that C is less than five. So like always, pause this video and have a go at it. And even if you struggle with it, that's even, that's better, your brain will be more primed for the actual solution that we can go through together. All right. So I'm assuming you've had a go at it. So there'... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
All right. So I'm assuming you've had a go at it. So there's a couple of ways to approach it. You could say, well look, this is just gonna be the probability that C is equal to one plus the probability that C is equal to two plus the probability that C is equal to three plus the probability that C is equal to four. And... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
You could say, well look, this is just gonna be the probability that C is equal to one plus the probability that C is equal to two plus the probability that C is equal to three plus the probability that C is equal to four. And we can calculate it this way. What is the probability that C equals one? Well, it's the proba... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
Well, it's the probability that her very first order is a telephone order. And so we'll have 0.1. What's the probability that C equals two? Well, it's the probability that her first order is not a telephone order. So it's one minus 10%. There's a 90% chance it's not a telephone order. And that her second order is a tel... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
Well, it's the probability that her first order is not a telephone order. So it's one minus 10%. There's a 90% chance it's not a telephone order. And that her second order is a telephone order. What about the probability C equals three? Well, her first two orders would not be telephone orders and her third order would ... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
And that her second order is a telephone order. What about the probability C equals three? Well, her first two orders would not be telephone orders and her third order would be one. And then C equals four? Well, her first three orders would not be telephone orders and her fourth one would. And we could get a calculator... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
And then C equals four? Well, her first three orders would not be telephone orders and her fourth one would. And we could get a calculator maybe and add all of these things up and we would actually get the answer. But you're probably wondering, well, this is kinda hairy to type into a calculator. Maybe there is an easi... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
But you're probably wondering, well, this is kinda hairy to type into a calculator. Maybe there is an easier way to tackle this. And indeed, there is. So think about it. The probability that C is less than five, that's the same thing as one minus the probability that we don't have a telephone order in the first four. O... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
So think about it. The probability that C is less than five, that's the same thing as one minus the probability that we don't have a telephone order in the first four. One minus the probability that no telephone order in first four orders. So what's this? Well, because this is just saying, what's the probability we do ... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
So what's this? Well, because this is just saying, what's the probability we do have an order in the first four? So it's the same thing as one minus the probability that we don't have an order in the first four. And this is pretty straightforward to calculate. So this is going to be equal to one minus, and let me do th... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
And this is pretty straightforward to calculate. So this is going to be equal to one minus, and let me do this in another color so we know what I'm referring to. So what's the probability that we have no telephone orders in the first four orders? Well, the probability on a given order that you don't have a telephone or... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
Well, the probability on a given order that you don't have a telephone order is 0.9. And then if that has to be true for the first four, well, it's gonna be 0.9 times 0.9 times 0.9 times 0.9, or 0.9 to the fourth power. So this is a lot easier to calculate. So let's do that. Let's get a calculator out. All right, so le... | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
So let's do that. Let's get a calculator out. All right, so let me just take 0.9 to the fourth power is equal to, and then let me subtract that from one. So let me make that a negative, and then let me add one to it. And we get, there you go, 0.3439. So this is equal to 0.3439. And we're done. | Cumulative geometric probability (less than a value) AP Statistics Khan Academy.mp3 |
I have a 70% chance of making any free throw, which is actually higher than my actual free throw probability, which might be a surprise to you. But we said in that circumstance, if it's a 70% chance of making it, well that means that you have a one minus 70%, or 30% chance of missing. And we said if you took six attemp... | Generalizing k scores in n attempts Probability and Statistics Khan Academy.mp3 |
So this was just one particular situation, but we could generalize based on the logic that we had in that video. In fact, let's do that. So if I were to generalize it, if I were to say the probability, the probability, it's the exact same logic, of exactly, now let's say K, let me do this in a color, an interesting col... | Generalizing k scores in n attempts Probability and Statistics Khan Academy.mp3 |
So exactly two K scores, in N attempts, let's just say in N attempts, in N, and let me go back to that green color, N attempts, is going to be equal to, well, how many ways can you pick K things out of N, or N choose K, N choose K, and then, actually let's just generalize it even more. Let's just say that you have, you... | Generalizing k scores in n attempts Probability and Statistics Khan Academy.mp3 |
So if F is your probability of making a free throw, so if you want N scores, then this is going to be, this is going to be, well, it's going to be F to the N power, and then you're going to have, and then you're going to miss the remainder, sorry, F to the K power, because you're making exactly K scores. So F to the K ... | Generalizing k scores in n attempts Probability and Statistics Khan Academy.mp3 |
And we are going to think about the means of these populations. So let's say this first population is a population of golden retrievers, and this second population is a population of chihuahuas. And the mean that we're going to think about is maybe the mean weight. So mu one would be the true mean weight of the populat... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
So mu one would be the true mean weight of the population of golden retrievers, and mu two would be the true mean weight of the population of chihuahuas. And what we wanna think about is what is the difference between these two population means, between these two population parameters? Well, if we don't know this, all ... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And that's what we're going to talk about in this video. So how do we go about doing it? Well, we've seen this or similar things before. What you would do is you would take a sample from both populations, so from population one here, I would take a sample of size N sub one, and from that, I can calculate a sample mean.... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
What you would do is you would take a sample from both populations, so from population one here, I would take a sample of size N sub one, and from that, I can calculate a sample mean. So this is a statistic that is trying to estimate that. And I can also calculate a sample standard deviation. And I can do the same thin... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And I can do the same thing in the population of chihuahuas, if that's what our population two is all about. So I could take a sample, and actually, this sample does not have to be the same as N one, so I'll call it N sub two. It could be, but it doesn't have to be. And from that, I can calculate a sample mean, X bar s... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And from that, I can calculate a sample mean, X bar sub two, and a sample standard deviation. So now, assuming that our conditions for inference are met, and we've talked about those before, we have the random condition, we have the normal condition, we have the independence condition. Assuming those conditions are met... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And so you might say, all right, well, that would be the difference of my sample means, X bar sub one minus X bar sub two, plus or minus some Z value times my standard deviation, times the standard deviation of the sampling distribution of the difference of the sample means. So X bar sub one minus X bar sub two. And yo... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
Well, our confidence level would determine that. Confidence, confidence level. If our confidence level is 95%, that would determine our Z. Now, this would not be incorrect, but we face a problem, because we are going to need to estimate what the standard deviation of the sampling distribution of the difference between ... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
Now, this would not be incorrect, but we face a problem, because we are going to need to estimate what the standard deviation of the sampling distribution of the difference between our sample means actually is. To make that clear, let me write it this way. So the variance of the sampling distribution of the difference ... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
Now, if we knew the true underlying standard deviations of this population and this population, then we could actually come up with these. In that case, this right over here would be equal to the variance of the population, of population one, divided by our sample size, N one, plus, plus the variance of the underlying ... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
So we estimate them with our sample standard deviations. So we say this is going to be approximately equal to our first sample standard deviation squared over N one, plus our second sample standard deviation squared over N two. And so we can say that an estimate of the standard deviation of the sampling distribution of... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
It's going to be approximately equal to the square root of S one squared over N one, plus S two squared over N two. But the problem is, is once we use this estimate that we can figure out, a critical Z value isn't going to be as good as a critical T value. So instead, you would say my confidence interval is going to be... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And so you have T star times our estimate of this, which is going to be equal to the square root of S sub one squared over N one, plus S sub two squared over N two. And then you might say, well, what determines our T star? Well, once again, you would look it up on a table using your confidence level, and you might be s... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
When I look up a T value, I don't just care about a confidence level, I also care about degrees of freedom. What is going to be the degrees of freedom in this situation? Well, there's a simple answer and a complicated answer. Once we think about the difference of means, there's fairly sophisticated formulas that comput... | Constructing t interval for difference of means AP Statistics Khan Academy.mp3 |
And we have four of them right over here, and the first thing I want to think about is if we can approximate what value would be the middle value, or the median for the data set described by these density curves. So just to remind ourselves, if we have a set of numbers and we order them from least to greatest, the medi... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
So when you're looking at a density curve, you'd want to look at the area, and you'd want to say, okay, at what value do we have equal area above and below that value? And so for this one, just eyeballing it, this value right over here would be the median. And in general, if you have a symmetric distribution like this,... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Here we have a slightly more unusual distribution. This would be called a bimodal distribution, but you have two major lumps right over here. But it is symmetric, and that point of symmetry is right over here, and so this value, once again, would be the median. Another way to think about it is the area to the left of t... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Another way to think about it is the area to the left of that value is equal to the area to the right of that value, making it the median. What if we're dealing with non-symmetric distributions? Well, we'd want to do the same principle. We'd want to think at what value is the area on the right and the area on the left ... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
We'd want to think at what value is the area on the right and the area on the left equal? And once again, this isn't going to be super exact, but I'm going to try to approximate it. You might be tempted to go right at the top of this lump right over here, but if I were to do that, it's pretty clear, even eyeballing it,... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
So that would not be the median. If I move the median a little bit over to the right, this may be right around here, this looks a lot closer. Once again, I'm approximating it, but it's reasonable to say that the area here looks pretty close to the area right over there, and if that is the case, then this is going to be... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Similarly, on this one right over here, maybe right over here. And once again, I'm just approximating it, but that seems reasonable, that this area is equal to that one. Even though this is longer, it's much lower. This part of the curve is much higher, even though it goes on less to the right. So that's the median. Fo... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
This part of the curve is much higher, even though it goes on less to the right. So that's the median. For well-behaved continuous distributions like this, it's going to be the value for which the area to the left and the area to the right are equal. But what about the mean? Well, the mean is you take each of the possi... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
But what about the mean? Well, the mean is you take each of the possible values and you weight it by their frequencies, you weight it by their frequencies, and you add all of that up. And so for symmetric distributions, your mean and your median are actually going to be the same. So this is going to be your mean as wel... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
So this is going to be your mean as well, this is going to be your mean as well. If you wanna think about it in terms of physics, the mean would be your balancing point, the point at which you would wanna put a little fulcrum and you would wanna balance the distribution. And so you could put a little fulcrum here and y... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
This thing would balance. And that all comes out of this idea of the weighted average of all of these possible values. What about for these less symmetric distributions? Well, let's think about it over here. Where would I have to put the fulcrum? Or what does our intuition say if we wanted to balance this? Well, we hav... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Well, let's think about it over here. Where would I have to put the fulcrum? Or what does our intuition say if we wanted to balance this? Well, we have equal areas on either side, but when you have this long tail to the right, it's going to pull the mean to the right of the median in this case. And so our balance point... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Well, we have equal areas on either side, but when you have this long tail to the right, it's going to pull the mean to the right of the median in this case. And so our balance point is probably going to be something closer to that. And once again, this is me approximating it, but this would roughly be our mean. It wou... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
It would sit in this case to the right of our median. Let me make it clear. This median is referring to that, the mean is referring to this. In this case, because I have this long tail to the left, it's likely that I would have to balance it out right over here. So the mean would be this value right over there. And the... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
In this case, because I have this long tail to the left, it's likely that I would have to balance it out right over here. So the mean would be this value right over there. And there's actually a term for these non-symmetric distributions where the mean is varying from the median. Distributions like this are referred to... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
Distributions like this are referred to as being skewed. And this distribution, where you have the mean to the right of the median, where you have this long tail to the right, this is called right skewed. Now, the technical idea of skewness can get quite complicated, but generally speaking, you can spot it out when you... | Median, mean and skew from density curves AP Statistics Khan Academy.mp3 |
I'm pretty sure I just tore my calf muscle this morning while sprinting with my son, but the math must not stop. So I'm here to help us think about what we could call influential points when we're thinking about regressions. And to help us here, I have this tool from BFW Publishing. I encourage you to go here and use t... | Influential points in regression AP Statistics Khan Academy.mp3 |
I encourage you to go here and use this tool yourself. But what it allows us to do is to draw some points. So just like that, let me draw some points, and then fit a least squares line. So that's the least squares line right over there. And you can not only see the line, we can see our correlation coefficient. It's pre... | Influential points in regression AP Statistics Khan Academy.mp3 |
So that's the least squares line right over there. And you can not only see the line, we can see our correlation coefficient. It's pretty good, 0.8156. It's pretty close to one. So we have a pretty good fit right over here. But what we're gonna think about are points that might influence, or might be overly influential... | Influential points in regression AP Statistics Khan Academy.mp3 |
It's pretty close to one. So we have a pretty good fit right over here. But what we're gonna think about are points that might influence, or might be overly influential, we could say, to different aspects of this regression line. So one type of influential point is known as an outlier. And a good way of identifying an ... | Influential points in regression AP Statistics Khan Academy.mp3 |
So one type of influential point is known as an outlier. And a good way of identifying an outlier is it's a very bad fit to the line, or it has a very large residual. And so if I put a point right over here, that is an outlier. So what happens when we have an outlier like that? So before we had a correlation coefficien... | Influential points in regression AP Statistics Khan Academy.mp3 |
So what happens when we have an outlier like that? So before we had a correlation coefficient of 0.8 something, you put one outlier like that, it's now one out of 16 points, it dramatically lowered our correlation coefficient because we have a really large residual right over here. So an outlier like this has been very... | Influential points in regression AP Statistics Khan Academy.mp3 |
It didn't impact the slope of the line a tremendous amount. It did a little bit. Actually, when I put it there, it didn't impact the slope much at all. And it does impact the y-intercept a little bit. Actually, when I put it out here, it doesn't impact the y-intercept much at all. If I put it a little bit more to the l... | Influential points in regression AP Statistics Khan Academy.mp3 |
And it does impact the y-intercept a little bit. Actually, when I put it out here, it doesn't impact the y-intercept much at all. If I put it a little bit more to the left, it impacts it a little bit. But these outliers that are at least close to the mean x-value, these seem to be most relevant in terms of impacting or... | Influential points in regression AP Statistics Khan Academy.mp3 |
But these outliers that are at least close to the mean x-value, these seem to be most relevant in terms of impacting or most influential in terms of the correlation coefficient. Now, what about an outlier that's further away from the mean x-value? And something, a point whose x-value is further away from the mean x-val... | Influential points in regression AP Statistics Khan Academy.mp3 |
And the way you could think about that is if you imagine this as being some type of a seesaw somehow pivoted on the mean x-value, well, if you put a point out here, it looks like it's pivoting down. It's like someone's sitting at this end of the seesaw. And so that's where I think the term leverage comes from. And you ... | Influential points in regression AP Statistics Khan Academy.mp3 |
And you can see when I put an outlier, if I put a high leverage outlier out here, that does many things. It definitely drops the correlation coefficient. It changes the slope, and it changes the y-intercept. So it does a lot of things. So it's highly influential for everything I just talked about. Now, if I have a high... | Influential points in regression AP Statistics Khan Academy.mp3 |
So it does a lot of things. So it's highly influential for everything I just talked about. Now, if I have a high leverage point that's maybe a little bit less of an outlier, something like this, based on the points that I happen to have, it didn't hurt the correlation coefficient. In fact, in that example, it's actuall... | Influential points in regression AP Statistics Khan Academy.mp3 |
In fact, in that example, it's actually improved it a little bit, but it did change the y-intercept a bit, and it did change the slope a bit, although obviously not as dramatic as when you do something like that. And that kills the correlation coefficient as well. Let's see what happens if we do things over here. So if... | Influential points in regression AP Statistics Khan Academy.mp3 |
So if I have a high leverage outlier over here, you see the same thing. A high leverage outlier seems to influence everything. If it is a high leverage point that is less of an outlier, actually, once again, it improved the correlation coefficient. You could say that it's still influential on the correlation coefficien... | Influential points in regression AP Statistics Khan Academy.mp3 |
What I wanna do in this video is give a primer on thinking about when to use a z statistic versus a t statistic when we are doing significance tests. So there's two major scenarios that we will see in an introductory statistics class. One is when we are dealing with proportions. So I'll write that on the left side righ... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
So I'll write that on the left side right over here. And the other is when we are dealing with means. In the proportion case, when we're doing our significance test, we will set up some null hypothesis that usually deals with the population proportion. We might say it is equal to some value. Let's just call that P sub ... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
We might say it is equal to some value. Let's just call that P sub one. And then maybe you have an alternative hypothesis that well, no, the population proportion is greater than that or less than that or it's just not equal to that. So let me just go with that one. It's not equal to P sub one. And then what we do to a... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
So let me just go with that one. It's not equal to P sub one. And then what we do to actually test, to actually do the significance test is we take a sample from the population. It's going to have a sample size of N. We need to make sure that we feel good about making the inference. We've talked about the conditions fo... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
It's going to have a sample size of N. We need to make sure that we feel good about making the inference. We've talked about the conditions for inference in previous videos multiple times. But from this, we calculate the sample proportion. And then from this, we calculate the P value. And the way that we do the P value... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
And then from this, we calculate the P value. And the way that we do the P value, remember, the P value is the probability of getting a sample proportion at least this extreme. And if it's below some threshold, we reject the null hypothesis and it suggests the alternative. And over here, the way we do that is we find a... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
And over here, the way we do that is we find an associated Z value for that P, for that sample proportion. And the way that we calculate it, we say, okay, look, our Z is going to be how many of the sampling distributions, standard deviations, are we away from the mean? And remember, the mean of the sampling distributio... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
So here, we got this sample statistic, this sample proportion. The difference between that and the assumed proportion, remember, when we do these significance tests, we try to figure out the probability assuming the null hypothesis is true. And so when we see this P sub zero, this is the assumed proportion from the nul... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
So that's the difference between these two, the sample proportion and the assumed proportion. And then you'd wanna divide it by what's often known as the standard error of the statistic, which is just the standard deviation of the sampling distribution of the sample proportion. And this works out well for proportions b... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
This is going to be equal to the square root of the assumed population proportion times one minus the assumed population proportion, all of that over N. And then I would use this Z statistic to figure out the P value. And in this case, I would look at both tails of the distribution because I care about how far I am eit... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
You will make a null hypothesis. Maybe you assume the population mean is equal to mu one. And then there's going to be an alternative hypothesis that maybe your population mean is not equal to mu one. And you're gonna do something very simple. You take your population, take a sample of size N. Instead of calculating a ... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
And you're gonna do something very simple. You take your population, take a sample of size N. Instead of calculating a sample proportion, you calculate a sample mean. And actually, you can calculate other things like a sample standard deviation. But now you have an issue. You say, well, ideally, I would use a Z statist... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
But now you have an issue. You say, well, ideally, I would use a Z statistic. And you could if you were able to say, well, I could take the difference between my sample mean and the assumed mean in the null hypothesis. So that would be this right over here. That's what that zero means, the assumed mean from the null hy... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
So that would be this right over here. That's what that zero means, the assumed mean from the null hypothesis. And I would then divide by the standard error of the mean, which is another way of saying the standard deviation of the sampling distribution of the sample mean. But this is not so easy to figure out. In order... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
But this is not so easy to figure out. In order to figure out this, this is going to be the standard deviation of the underlying population divided by the square root of N. We know what N is going to be if we conducted the sample, but we don't know what the standard deviation is. So instead, what we do is we estimate t... | When to use z or t statistics in significance tests AP Statistics Khan Academy.mp3 |
Alright, so it says that, so it says 20 people said their favorite type of movie was comedy. Six people said their favorite type of movie was scary. 10 people said their favorite type of movie was adventure. 10 people also said their favorite type of movie is cartoons. And then 16 people said their favorite type of mov... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
10 people also said their favorite type of movie is cartoons. And then 16 people said their favorite type of movie is a mystery. Alright, so let's read the questions here. So which of the following types of movies were picked by fewer than 14 people? So fewer than 14 people. So more than 14 picked comedy or mystery. So... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
So which of the following types of movies were picked by fewer than 14 people? So fewer than 14 people. So more than 14 picked comedy or mystery. So this line right over here would be 14. So fewer than 14 were scary, adventure, or cartoon. This was six people, 10 people, and 10 people. Scary, adventure, and cartoon. | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
So this line right over here would be 14. So fewer than 14 were scary, adventure, or cartoon. This was six people, 10 people, and 10 people. Scary, adventure, and cartoon. So we want to pick scary, adventure, and cartoon. These three had less than 14 people pick them. So let's do a couple more of these. | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
Scary, adventure, and cartoon. So we want to pick scary, adventure, and cartoon. These three had less than 14 people pick them. So let's do a couple more of these. Let's do a couple more. Puppy Party Place graphed the number of dogs that came in each weekday. So let's see, 80 dogs came in on Monday, 160 dogs came in on... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
So let's do a couple more of these. Let's do a couple more. Puppy Party Place graphed the number of dogs that came in each weekday. So let's see, 80 dogs came in on Monday, 160 dogs came in on Tuesday, 80 dogs came in on Wednesday, 140 dogs came in on Thursday, and then Friday was a very popular day. 180 dogs came into... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
So let's see, 80 dogs came in on Monday, 160 dogs came in on Tuesday, 80 dogs came in on Wednesday, 140 dogs came in on Thursday, and then Friday was a very popular day. 180 dogs came into the Puppy Party Place on Friday. Alright, so what are they asking us? On which day did the same number of dogs come to Puppy Party ... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
On which day did the same number of dogs come to Puppy Party Place as on Monday and Wednesday combined? Alright, so let's see, Monday and Wednesday combined. So on Monday we had 80 puppies come there, or 80 dogs, and on Wednesday we had 80 dogs. And they're saying which day had the same as Monday and Wednesday combined... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
And they're saying which day had the same as Monday and Wednesday combined? So Monday and Wednesday combined would be 80 plus 80, which would be 160. So on which of these days did 160 dogs come? Well, we see it right over here, 160 dogs. That was on Tuesday, and only on Tuesday. So Tuesday. Let's do a few more of these... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
Well, we see it right over here, 160 dogs. That was on Tuesday, and only on Tuesday. So Tuesday. Let's do a few more of these. Desert Zone asked its customers about their favorite ice cream flavor and graphed the results. So 175 customers said vanilla, 225 said chocolate, 75 said strawberry, and 200 said cookie dough. ... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
Let's do a few more of these. Desert Zone asked its customers about their favorite ice cream flavor and graphed the results. So 175 customers said vanilla, 225 said chocolate, 75 said strawberry, and 200 said cookie dough. Alright, how many more customers picked the most popular flavor than the least popular flavor? Al... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
Alright, how many more customers picked the most popular flavor than the least popular flavor? Alright, so the most popular flavor was chocolate. That was 225. And the least popular flavor, it's late, to the least popular flavor, it's a tongue twister, was 75. So how many more picked the most popular than the least pop... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
And the least popular flavor, it's late, to the least popular flavor, it's a tongue twister, was 75. So how many more picked the most popular than the least popular? Well, the most popular is 225, the least popular was 75. So it's 225 minus 75. Let's see, 225 minus 25 would be 200, minus 50 would be 175, minus 75 would... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
So it's 225 minus 75. Let's see, 225 minus 25 would be 200, minus 50 would be 175, minus 75 would be 150. So we get 150 customers. And once again, we're saying that 150 more customers picked chocolate, the most popular flavor, than the least popular. Another way you could do it is you could look at the least popular an... | More solving problems with bar graphs Fractions 3rd grade Khan Academy.mp3 |
The scatter plot and trend line below show the relationship between how many hours students spent studying and their score on the test. The line fitted to model the data has a slope of 15. So the line that they're talking about is right here. So this is the scatter plot. This shows that some student who spent some time... | Interpreting slope of regression line AP Statistics Khan Academy.mp3 |
So this is the scatter plot. This shows that some student who spent some time between half an hour and an hour studying got a little bit less than a 45 on the test. The student here who got a little bit higher than a 60 spent a little under two hours studying. This student over here who looks like they got like a 94 or... | Interpreting slope of regression line AP Statistics Khan Academy.mp3 |
This student over here who looks like they got like a 94 or a 95 spent over four hours studying. And so then they fit a line to it and this line has a slope of 15. And before I even read these choices, what's the best interpretation of this slope? Well, if you think this line is indicative of the trend and it does look... | Interpreting slope of regression line AP Statistics Khan Academy.mp3 |
Well, if you think this line is indicative of the trend and it does look like that from the scatter plot, that implies that roughly every extra hour that you study is going to improve your score by 15. You could say on average according to this regression. So if we start over here and we were to increase by one hour ou... | Interpreting slope of regression line AP Statistics Khan Academy.mp3 |
And it does indeed look like that. We're going from, we're going in the horizontal direction, we're going one hour, and then in the vertical direction we're going from 45 to 60. So that's how I would interpret it. Every hour, based on this regression, you could, it's not unreasonable to expect 15 points improvement, or... | Interpreting slope of regression line AP Statistics Khan Academy.mp3 |
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