Sentence stringlengths 102 3.15k | video_title stringlengths 51 104 |
|---|---|
If the P value is less than our significance level, then we reject, reject our null hypothesis, and that would suggest the alternative. If this is not true, then we would fail to reject the null hypothesis. So let's look at these choices. And if you didn't answer it the first time, I encourage you to pause the video ag... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
And if you didn't answer it the first time, I encourage you to pause the video again. So at the alpha is equal to 0.01 significance level, they should conclude that more than 50% of adults support the tax increase. So if the alpha is 1 hundredth, the P value right over here is over 3 hundredths. It's roughly 3.3%. So t... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
It's roughly 3.3%. So this is a situation where our P value, our P value is greater than or equal to alpha. In fact, it's definitely greater than alpha here. And so here we would fail to reject, we would fail to reject our null hypothesis. And so we wouldn't conclude that more than 50% of adults support the tax increas... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
And so here we would fail to reject, we would fail to reject our null hypothesis. And so we wouldn't conclude that more than 50% of adults support the tax increase. Because remember, our null hypothesis is that 50% do, and we're failing to reject this. So that's not gonna be true. At that same significance level, they ... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
So that's not gonna be true. At that same significance level, they should conclude that less than 50% of adults support the tax increase. No, we can't say that either. We just failed to reject this null hypothesis, that the true proportion is 50%. At the alpha is equal to, so at the alpha equals to 5 hundredth signific... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
We just failed to reject this null hypothesis, that the true proportion is 50%. At the alpha is equal to, so at the alpha equals to 5 hundredth significance level, they should conclude that more than 50% of adults support the tax increase. Well yeah, in this situation, we have our P value, which is 0.033. It is indeed ... | Making conclusions in a test about a proportion AP Statistics Khan Academy.mp3 |
What I have here is the list of ages of the students in a class. And what I want to explore in this video is different ways of representing this data and then see if we can answer questions about the data. So the first way we can think about it is as a frequency table. Frequency table. Frequency table. And what we're g... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Frequency table. Frequency table. And what we're going to do is we're going to look at each, for each age, for each possible age that we've measured here to see how many students in the class are of that age. So we could say the age is one column. And then the number. The number of students of that age. Or we could eve... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So we could say the age is one column. And then the number. The number of students of that age. Or we could even say the frequency. Frequency. When people say, how frequent do you do something, they're saying, how often does it happen? How often do you do that thing? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Or we could even say the frequency. Frequency. When people say, how frequent do you do something, they're saying, how often does it happen? How often do you do that thing? Frequency. Or we could also say, actually, let me just write number. I'm always a fan of the simpler number at age, which we could also consider the... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
How often do you do that thing? Frequency. Or we could also say, actually, let me just write number. I'm always a fan of the simpler number at age, which we could also consider the frequency at that age. Frequency of students. All right. So what's the lowest age that we have here? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
I'm always a fan of the simpler number at age, which we could also consider the frequency at that age. Frequency of students. All right. So what's the lowest age that we have here? Well, the lowest age is five. So I'll start with five. And how many students in the class are age five? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So what's the lowest age that we have here? Well, the lowest age is five. So I'll start with five. And how many students in the class are age five? How frequent is the number five? Let's see. There is one, two. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And how many students in the class are age five? How frequent is the number five? Let's see. There is one, two. Let me keep scanning. Looks like there's only two fives. So I could write a two here. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
There is one, two. Let me keep scanning. Looks like there's only two fives. So I could write a two here. There are two fives. And now let's go to six. How many sixes are there? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So I could write a two here. There are two fives. And now let's go to six. How many sixes are there? Let's see. There is one sixth. There's only one six-year-old in the class. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
How many sixes are there? Let's see. There is one sixth. There's only one six-year-old in the class. All right. Seven-year-olds. See, there's one, two, three, four seven-year-olds. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
There's only one six-year-old in the class. All right. Seven-year-olds. See, there's one, two, three, four seven-year-olds. Now what about eight-year-olds? I'm going to do this in a color that I have not used yet. Eight-year-olds, we have no eight-year-olds. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
See, there's one, two, three, four seven-year-olds. Now what about eight-year-olds? I'm going to do this in a color that I have not used yet. Eight-year-olds, we have no eight-year-olds. Zero eight-year-olds. And then we have nine-year-olds. Let's see. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Eight-year-olds, we have no eight-year-olds. Zero eight-year-olds. And then we have nine-year-olds. Let's see. Nine-year-olds, we have one, two, three, four nine-year-olds. 10-year-olds, what do we have? We have one 10-year-old right over there. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Let's see. Nine-year-olds, we have one, two, three, four nine-year-olds. 10-year-olds, what do we have? We have one 10-year-old right over there. And then 11-year-olds. There are no 11-year-olds. And then let me scroll up a little bit. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
We have one 10-year-old right over there. And then 11-year-olds. There are no 11-year-olds. And then let me scroll up a little bit. And then finally 12-year-olds. 12-year-olds, there are one, two 12-year-olds. So what we have just constructed is a frequency table. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And then let me scroll up a little bit. And then finally 12-year-olds. 12-year-olds, there are one, two 12-year-olds. So what we have just constructed is a frequency table. It's a frequency table. You can see for each age how many students are at that age. So it's giving you the same information as we have up here. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So what we have just constructed is a frequency table. It's a frequency table. You can see for each age how many students are at that age. So it's giving you the same information as we have up here. You could take this table and construct what we have up here. You would just write down two fives, one sixth, four sevens... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So it's giving you the same information as we have up here. You could take this table and construct what we have up here. You would just write down two fives, one sixth, four sevens, no eights, four nines, one 10, no 11s, and two 12s. And then you would just have this list of numbers. Now a way to visually look at a fr... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And then you would just have this list of numbers. Now a way to visually look at a frequency table is a dot plot. So let me draw a dot plot right over here. So a dot plot. And a dot plot, we essentially just take the same information and even think about it the same way, but we just show it visually. So in a dot plot, ... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So a dot plot. And a dot plot, we essentially just take the same information and even think about it the same way, but we just show it visually. So in a dot plot, what we would have of, actually let me just not draw an even arrow there. We have the different age groups. So five, six, seven, eight, nine, 10, 11, and 12.... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
We have the different age groups. So five, six, seven, eight, nine, 10, 11, and 12. And we have a dot to represent, or we use a dot for each student at that age. So there's two five-year-olds, so I'll do two dots. One and two. There's one six-year-old, so that's going to be one dot right over here. There's four seven-y... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So there's two five-year-olds, so I'll do two dots. One and two. There's one six-year-old, so that's going to be one dot right over here. There's four seven-year-olds, so one, two, three, four dots. There's no eight-year-olds. There's four nine-year-olds, so one, two, three, and four. There's one 10-year-old, so let's ... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
There's four seven-year-olds, so one, two, three, four dots. There's no eight-year-olds. There's four nine-year-olds, so one, two, three, and four. There's one 10-year-old, so let's put a dot, one dot, right over there for that one 10-year-old. There's no 11-year-olds, so I'm not going to put any dots there. And then t... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
There's one 10-year-old, so let's put a dot, one dot, right over there for that one 10-year-old. There's no 11-year-olds, so I'm not going to put any dots there. And then there's two 12-year-olds. So one 12-year-old and another 12-year-old. So there you go. We have frequency table, dot plot, list of numbers. These are ... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So one 12-year-old and another 12-year-old. So there you go. We have frequency table, dot plot, list of numbers. These are all showing the same data, just in different ways. And once you have it represented in any of these ways, we can start to ask questions about it. So we could say, what is the most frequent age? Wel... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
These are all showing the same data, just in different ways. And once you have it represented in any of these ways, we can start to ask questions about it. So we could say, what is the most frequent age? Well, the most frequent age, when you look at it visually, or the easiest thing might be just look at the dot plot, ... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Well, the most frequent age, when you look at it visually, or the easiest thing might be just look at the dot plot, because you see it visually, the most frequent age are the two highest stacks. So there's actually seven and nine are tied for the most frequent age. You would have also seen it here, where seven and nine... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And if you just had this data, you'd have to count all of them to kind of come up with this again and say, OK, there's four sevens, four nines. That's the largest number. So if you're looking for what's the most frequent age, when you just visually inspect here, it probably pops out at you the fastest. But there's othe... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
But there's other questions we can ask ourselves. We can ask ourselves, what is the range of ages in the classroom? And this is, once again, where maybe the dot plot is the most, it jumps out at you the most, because the range is just the maximum age in your, or the maximum data point minus the minimum data point. So w... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So what's the maximum age here? Well, the maximum age here, we see it from the dot plot, is 12. And the minimum age here, you see, is five. So there's a range of seven. The difference between the maximum and the minimum is seven. But you could have also done that over here. You could say, hey, the maximum age here is 1... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
So there's a range of seven. The difference between the maximum and the minimum is seven. But you could have also done that over here. You could say, hey, the maximum age here is 12. Minimum age here is five. And so you find the difference between 12 and five, which is seven. Here, you still could have done it. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
You could say, hey, the maximum age here is 12. Minimum age here is five. And so you find the difference between 12 and five, which is seven. Here, you still could have done it. You could say, OK, what's the lowest? Let's look at five. Are there any fours here? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Here, you still could have done it. You could say, OK, what's the lowest? Let's look at five. Are there any fours here? Nope, there's no fours. So five's the minimum age. And what's the largest? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Are there any fours here? Nope, there's no fours. So five's the minimum age. And what's the largest? Is it seven? No, is it nine? Nine, not even 10? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And what's the largest? Is it seven? No, is it nine? Nine, not even 10? Oh, 12. 12. Are there any 13s? | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Nine, not even 10? Oh, 12. 12. Are there any 13s? No, 12 is the maximum. So you say 12 minus five is seven to get the range. But then we could ask ourselves other questions. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Are there any 13s? No, 12 is the maximum. So you say 12 minus five is seven to get the range. But then we could ask ourselves other questions. We could say, how many older than nine is a question we could ask ourselves. And then if we were to look at the dot plot, we say, OK, this is nine. And we care about how many ar... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
But then we could ask ourselves other questions. We could say, how many older than nine is a question we could ask ourselves. And then if we were to look at the dot plot, we say, OK, this is nine. And we care about how many are older than nine. So that would be this one, two, and three. Or you could look over here. How... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
And we care about how many are older than nine. So that would be this one, two, and three. Or you could look over here. How many are older than nine? Well, it's the one person who's 10, and then the two who are 12. So there are three. And over here, if you said how many are older than nine, well, then you would just ha... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
How many are older than nine? Well, it's the one person who's 10, and then the two who are 12. So there are three. And over here, if you said how many are older than nine, well, then you would just have to go through the list and say, OK, no, no, no, no, no, no, no, no. OK, here, one, two, three. And then not that pers... | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
Choose all answers that apply. Pause this video, have a go at that. All right, now let's go through each of these choices. So choice A says the probability that one of these tickets wins a prize is 0.95 on average. Well, I see where they're getting that 0.95. They're getting it from right over here, but that's not the ... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
So choice A says the probability that one of these tickets wins a prize is 0.95 on average. Well, I see where they're getting that 0.95. They're getting it from right over here, but that's not the probability that you're winning. That's the expected return. The probability that you win is much lower. If the odds are on... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
That's the expected return. The probability that you win is much lower. If the odds are one to 50, that means that the probability of winning is one to 51. So it's a much lower probability than this right over here. So definitely rule that out. Someone who buys this ticket is most likely to win 95 cents. That is not ne... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
So it's a much lower probability than this right over here. So definitely rule that out. Someone who buys this ticket is most likely to win 95 cents. That is not necessarily the case either. We don't know what the different outcomes are for the prize. It's very likely that there's no outcome for that prize where you wi... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
That is not necessarily the case either. We don't know what the different outcomes are for the prize. It's very likely that there's no outcome for that prize where you win exactly 95 cents. Instead, there's likely to be outcomes that are much larger than that with very low probabilities, and then when you take the weig... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
Instead, there's likely to be outcomes that are much larger than that with very low probabilities, and then when you take the weighted average of all of the outcomes, then you get an expected return of 95 cents. So it's actually maybe even impossible to win exactly 95 cents, so I would rule that out. If we looked at ma... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
That one feels pretty interesting because we're looking at many of these tickets, and so across many of them, you would expect to, on average, get the expected return as your return. And so this is what we are saying here. The average return would be about that, would be approximately that. So I like that choice. That ... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
So I like that choice. That is a good interpretation of expected value. And then choice D, if 1,000 people each bought one of these tickets, they'd expect a net gain of about $950 in total. This one is tempting. Instead of net gain, if it just said return, this would make a lot of sense. In fact, it would be completely... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
This one is tempting. Instead of net gain, if it just said return, this would make a lot of sense. In fact, it would be completely consistent with choice C. If you have 1,000 people, that would be many tickets, and if on average, if their average return is about 95 cents per ticket, then their total return would be abo... | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
But they didn't write return here. They wrote net gain. Net gain would be how much you get minus how much you paid. And 1,000 people would have to pay, if they each got a ticket, would pay $2,000. So they would pay 2,000. They would expect a return of $950. Their net gain would actually be negative $1,050. | Interpreting expected value Probability & combinatorics Khan Academy.mp3 |
After randomization, each child was asked to watch a cartoon in a private room, containing a large bowl of Goldfish crackers. The cartoon included two commercial breaks. The first group watched food commercials, mostly snacks, while the second group watched non-food commercials, games and entertainment products. Once t... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
Once the child finished watching the cartoon, the conductors of the experiment weighed the cracker bowls to measure how many grams of crackers the child ate. They found that the mean amount of crackers eaten by the children who watched food commercials is 10 grams greater than the mean amount of crackers eaten by the c... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
They took 500 children and then they randomly assigned them to two different groups. So you have group 1 over here and you have group 2. So let's say that this right over here is the first group. The first group watched food commercials. So this is group number 1. So they watched food commercials. We could call this th... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
The first group watched food commercials. So this is group number 1. So they watched food commercials. We could call this the treatment group. We're trying to see what's the effect of watching food commercials. And then they tell us the second group watched non-food commercials. So this is the control group. | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
We could call this the treatment group. We're trying to see what's the effect of watching food commercials. And then they tell us the second group watched non-food commercials. So this is the control group. So number 2, this is non-food commercials. So this is the control right over here. Once the child finished watchi... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So this is the control group. So number 2, this is non-food commercials. So this is the control right over here. Once the child finished watching the cartoon, for each child they weighed how much of the crackers they ate and then they took the mean of it and they found that the mean here, that the kids ate 10 grams gre... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
Once the child finished watching the cartoon, for each child they weighed how much of the crackers they ate and then they took the mean of it and they found that the mean here, that the kids ate 10 grams greater on average than this group right over here. Which, just looking at that data, makes you believe that somethi... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
But the question that you always have to ask yourself in a situation like this, well, isn't there some probability that this would have happened by chance? That even if you didn't make them watch the commercials, if these were just two random groups and you didn't make either group watch a commercial, you made them all... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So how do you figure out what's the probability that this could have happened, that the 10 grams greater in mean amount eaten here, that that could have just happened by chance? Well, the way you do it is what they do right over here. Using a simulator, they re-randomized the results into two new groups and measured th... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
They repeated the simulation 150 times and plotted the resulting differences as given below. So what they did is they said, okay, they have 500 kids, and each kid, they had 500 children, so number 1, 2, 3, all the way up to 500. And for each child, they measured how much was the weight of the crackers that they ate. So... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So maybe child 1 ate 2 grams, and child 2 ate 4 grams, and child 3 ate, I don't know, ate 12 grams, all the way to child number 500, ate, I don't know, maybe they didn't eat anything at all, ate 0 grams. And we already know, let's say, the first time around, 1 through 200, and 1 through, I guess we should, you know, th... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So now they're saying, okay, let's maybe put this person in group number 2, put this person in group number 2, and this person stays in group number 2, and this person stays in group number 1, and this person stays in group number 1. So now they're completely mixing up all of the results that they had, so it's complete... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So out of the 150 times that they repeated the simulation doing this little exercise here, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, I'm having trouble counting this, let's see, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, I keep, it's so small, I'm aging, but it looks like there's about, I don't know, high teens, a... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So it's not clear whether this is group 1 minus group 2 or group 2 minus group 1, but in either case, the situations where you have a 10-gram difference in mean, it's only 2 out of the 150 times. So when you do it randomly, when you just randomly put these results into two groups, the probability of the means being thi... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So that is on the order of 2%, or actually it's less than 2%. It's between 1 and 2%. And if you know that this is group, let's say that the situation we're talking about, let's say that this is group 1 minus group 2 in terms of how much was eaten, and so you're looking at this situation right over here, then that's onl... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
It happened less frequently than 1 in 100 times. It happened only 1 in 150 times. So if you look at that, you say, well, the probability, if this was just random, the probability of getting the results that you got is less than 1%. So to me, and then to most statisticians, that tells us that our experiment was signific... | Statistical significance of experiment Probability and Statistics Khan Academy.mp3 |
So I have some data here in a spreadsheet. You could use Microsoft Excel or you could use Google Spreadsheets. And we're gonna use the spreadsheet to quickly calculate some parameters. Let's say this is the population. Let's say this is, we're looking at a population of students and we wanna calculate some parameters, ... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Let's say this is the population. Let's say this is, we're looking at a population of students and we wanna calculate some parameters, and this is their ages, and we wanna calculate some parameters on that. And so, first I'm gonna calculate it using the spreadsheet. And then we're gonna think about how those parameters... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
And then we're gonna think about how those parameters change as we do things to the data. If we were to shift the data up or down, or if we were to multiply all the points by some value, what does that do to the actual parameters? So the first parameter I'm gonna calculate is the mean. Then I'm gonna calculate the stan... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Then I'm gonna calculate the standard deviation. Then I wanna calculate the median. And then I wanna calculate, let's say the interquartile range. Inter, I'll call it IQR. So let's do this. Let's first look at the measures of central tendency. So the mean, the function on most spreadsheets is the average function. | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Inter, I'll call it IQR. So let's do this. Let's first look at the measures of central tendency. So the mean, the function on most spreadsheets is the average function. And then I could use my mouse and select all of these, or I could press shift with my arrow button and select all of those. Okay, that's the mean of th... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So the mean, the function on most spreadsheets is the average function. And then I could use my mouse and select all of these, or I could press shift with my arrow button and select all of those. Okay, that's the mean of that data. Now let's think about what happens if I take all of that data and if I were to add a fix... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Now let's think about what happens if I take all of that data and if I were to add a fixed amount to it. So if I took all the data and if I were to add five to it. So an easy way to do that in a spreadsheet is you select that, you add five, and then I can scroll down. And notice, for every data point I had before, I no... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
And notice, for every data point I had before, I now have five more than that. So this is my new data set, which I'm calling data plus five. And let's see what the mean of that is. So the mean of that, notice, is exactly five more. And the same would have been true if I added or subtracted any number. The mean would ch... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So the mean of that, notice, is exactly five more. And the same would have been true if I added or subtracted any number. The mean would change by the amount that I add or subtract. And so, and that shouldn't surprise you, because when you're calculating the mean, you're adding all the numbers up and you're dividing by... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
And so, and that shouldn't surprise you, because when you're calculating the mean, you're adding all the numbers up and you're dividing by the numbers you have. And so, if all the numbers are five more, you're gonna add five, in this case, how many numbers are there? One, two, three, four, five, six, seven, eight, nine... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
You're gonna add 12 more fives and then you're gonna divide by 12, and so it makes sense that your mean goes up by five. Let's think about how the mean changes if you multiply. So if you take your data and if I were to multiply it times five, what happens? So this equals this times five. So now, all the data points are... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So this equals this times five. So now, all the data points are five times more. Now what happens to my mean? Notice, my mean is now five times as much. So the measures of central tendency, if I add or subtract, well, I'm gonna add or subtract the mean by that amount. And if I scale it up by five or if I scaled it down... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Notice, my mean is now five times as much. So the measures of central tendency, if I add or subtract, well, I'm gonna add or subtract the mean by that amount. And if I scale it up by five or if I scaled it down by five, well, my mean would scale up or down by that same amount. And if you numerically looked at how you c... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
And if you numerically looked at how you calculate a mean, it would make sense that this is happening mathematically. Now let's look at the other measure, the other typical measure of central tendency, and that is the median, to see if that has the same properties. So let's calculate the median here. So once again, you... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So once again, you wanna order these numbers and just find the middle number, which isn't too hard, but a computer can do it awfully fast. So that's the median for that data set. What do you think the median's gonna be if you take all of the data plus five? Well, the middle number, if you ordered all of these numbers a... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Well, the middle number, if you ordered all of these numbers and made them all five more, the orders, you could think of it as being the same order, but now the one in the middle is gonna be five more. So this should be 10.5. And yes, it is indeed 10.5. And what would happen if you multiply everything by five? Well, on... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
And what would happen if you multiply everything by five? Well, once again, you still have the same ordering, and so it should just multiply that by five. Yep, the middle number is now gonna be five times larger. So both of these measures of central tendency, if you shift all the data points or if you scale them up, yo... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So both of these measures of central tendency, if you shift all the data points or if you scale them up, you're going to similarly shift or scale up these measures of central tendency. Now let's think about these measures of spread. See if that's the same with these measures of spread. So standard deviation. So S-T-D-E... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So standard deviation. So S-T-D-E-V, I'm gonna take the population standard deviation. I'm assuming that this is my entire population. So let me, why is it, so let me make sure I'm doing, so standard deviation of all of this is going to be 2.99. Let's see what happens when I shift everything by five. Actually, pause th... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So let me, why is it, so let me make sure I'm doing, so standard deviation of all of this is going to be 2.99. Let's see what happens when I shift everything by five. Actually, pause the video. What do you think is going to happen? This is a measure of spread. So if you shift, I'll tell you what I think. If I shift eve... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
What do you think is going to happen? This is a measure of spread. So if you shift, I'll tell you what I think. If I shift everything by the same amount, the mean shifts, but the distance of everything from the mean should not change. So the standard deviation should not change, I don't think, in this example. And inde... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
If I shift everything by the same amount, the mean shifts, but the distance of everything from the mean should not change. So the standard deviation should not change, I don't think, in this example. And indeed, it does not change. So if we shift the data sets, in this case we shifted it up by five, or if we shifted it... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So if we shift the data sets, in this case we shifted it up by five, or if we shifted it down by one, your measure of spread, in this case standard deviation, should not change, or at least the standard deviation measure of spread does not change. But if we scale it, well, I think it should change, because you can imag... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
If I multiply this by five. So scaling the data set will scale the standard deviation in a similar way. What about interquartile range? Where it's essentially we're taking the third quartile and subtracting from that the first quartile to figure out kind of the range of the middle 50%. And so let's do that. We can have... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Where it's essentially we're taking the third quartile and subtracting from that the first quartile to figure out kind of the range of the middle 50%. And so let's do that. We can have the quartile function equals quartile, and then we wanna look at our data, and we want the third quartile. So that's gonna calculate th... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So that's gonna calculate the third quartile minus quartile, same data set. So now we wanna select it again. So same data set, but this is now gonna be the first quartile. So this is gonna give us our interquartile range. This is the, calculates the third quartile on that data set, and this calculates the first quartil... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
So this is gonna give us our interquartile range. This is the, calculates the third quartile on that data set, and this calculates the first quartile on that data set. And we get 2.75. Now let's think about what the inter, whether the interquartile range should change. And I don't think it will, because remember, every... | How parameters change as data is shifted and scaled AP Statistics Khan Academy.mp3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.