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One seven-year-old at the party. Well, this first possibility that we looked at, that was the case. There was only one seven-year-old at the party, and there was one 16-year-old at the party. And actually, that was the next statement. There's only one 16-year-old at the party. So both of these seem like we can definitely construct data that's consistent with this box plot, box and whiskers plot, where this is true. But could we construct one where it's not true? | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And actually, that was the next statement. There's only one 16-year-old at the party. So both of these seem like we can definitely construct data that's consistent with this box plot, box and whiskers plot, where this is true. But could we construct one where it's not true? Well, sure. Let's imagine, let's see, we have our median at 13. Median at 13. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
But could we construct one where it's not true? Well, sure. Let's imagine, let's see, we have our median at 13. Median at 13. And then we have, let's see, one, two, three, four, five. This is going to be the 10, the median of this bottom half. This is going to be 15. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Median at 13. And then we have, let's see, one, two, three, four, five. This is going to be the 10, the median of this bottom half. This is going to be 15. This is going to be 7. This is going to be 16. Well, this could also be 7. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This is going to be 15. This is going to be 7. This is going to be 16. Well, this could also be 7. It doesn't have to be. It could be 7, 8, 9, or 10. This could also be 16. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, this could also be 7. It doesn't have to be. It could be 7, 8, 9, or 10. This could also be 16. It doesn't have to be. It could be 15 as well. But just like that, I've constructed a data set. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This could also be 16. It doesn't have to be. It could be 15 as well. But just like that, I've constructed a data set. And these could be 10, 11, 12, 13. This could be 10, 11, 12, 13. This could be 13, 14, 15. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
But just like that, I've constructed a data set. And these could be 10, 11, 12, 13. This could be 10, 11, 12, 13. This could be 13, 14, 15. This one also could be 13, 14, 15. But the simple thing is, or the basic idea here, I can have a data set where I have multiple 7's and multiple 16's. Or I could have a data set where I only have one 7, or only one 16. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This could be 13, 14, 15. This one also could be 13, 14, 15. But the simple thing is, or the basic idea here, I can have a data set where I have multiple 7's and multiple 16's. Or I could have a data set where I only have one 7, or only one 16. So both of these statements, we just plain don't know. Now the next statement, exactly half the students are older than 13. Well, if you look at this possibility up here, we saw that 3 out of the 7 are older than 13. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Or I could have a data set where I only have one 7, or only one 16. So both of these statements, we just plain don't know. Now the next statement, exactly half the students are older than 13. Well, if you look at this possibility up here, we saw that 3 out of the 7 are older than 13. So that's not exactly half. 3 7's is not 1 half. But in this one over here, we did see that exactly half are older than 13. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, if you look at this possibility up here, we saw that 3 out of the 7 are older than 13. So that's not exactly half. 3 7's is not 1 half. But in this one over here, we did see that exactly half are older than 13. In fact, if you're saying exactly half, well, in this one, we're saying that exactly half are older than 13. We have an even number right over here. So it is exactly half. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
But in this one over here, we did see that exactly half are older than 13. In fact, if you're saying exactly half, well, in this one, we're saying that exactly half are older than 13. We have an even number right over here. So it is exactly half. So it's possible that it's true. It's possible that it's not true based on the information given. We once again do not know. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
So it is exactly half. So it's possible that it's true. It's possible that it's not true based on the information given. We once again do not know. Anyway, hopefully you found this interesting. The whole point of me doing this is, when you look at statistics, sometimes it's easy to kind of say, OK, I think it roughly means that. And that's sometimes OK. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We once again do not know. Anyway, hopefully you found this interesting. The whole point of me doing this is, when you look at statistics, sometimes it's easy to kind of say, OK, I think it roughly means that. And that's sometimes OK. But it's very important to think about what types of actual statements you can make and what you can't make. And it's very important when you're looking at statistics to say, well, you know what? I just don't know that the data actually is not telling me that thing for sure. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And as we begin our journey into the world of statistics, we will be doing a lot of what we can call descriptive statistics. So if we have a bunch of data, and if we want to tell something about all of that data without giving them all of the data, can we somehow describe it with a smaller set of numbers? So that's what we're going to focus on. And then once we build our toolkit on the descriptive statistics, then we can start to make inferences about that data, start to make conclusions, start to make judgments, and we'll start to do a lot of inferential, inferential statistics, make inferences. So with that out of the way, let's think about how we can describe the data. So let's say we have a set of numbers. We can consider this to be data. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
And then once we build our toolkit on the descriptive statistics, then we can start to make inferences about that data, start to make conclusions, start to make judgments, and we'll start to do a lot of inferential, inferential statistics, make inferences. So with that out of the way, let's think about how we can describe the data. So let's say we have a set of numbers. We can consider this to be data. Maybe we're measuring the heights of our plants in our garden. And let's say we have six plants, and the heights are four inches, three inches, one inch, six inches, and another one's one inch, and then another one is seven inches. And let's say someone just said, in another room, not looking at your plants, just said, well, you know, how tall are your plants? | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
We can consider this to be data. Maybe we're measuring the heights of our plants in our garden. And let's say we have six plants, and the heights are four inches, three inches, one inch, six inches, and another one's one inch, and then another one is seven inches. And let's say someone just said, in another room, not looking at your plants, just said, well, you know, how tall are your plants? And they only want to hear one number. They want to somehow have one number that represents all of these different heights of plants. How would you do that? | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
And let's say someone just said, in another room, not looking at your plants, just said, well, you know, how tall are your plants? And they only want to hear one number. They want to somehow have one number that represents all of these different heights of plants. How would you do that? Well, you'd say, well, how can I find something that maybe I want a typical number, maybe I want some number that somehow represents the middle, maybe I want the most frequent number, maybe I want the number that somehow represents the center of all of these numbers. And if you said any of those things, you would actually have done the same things that the people who first came up with descriptive statistics said. They said, well, how can we do it? | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
How would you do that? Well, you'd say, well, how can I find something that maybe I want a typical number, maybe I want some number that somehow represents the middle, maybe I want the most frequent number, maybe I want the number that somehow represents the center of all of these numbers. And if you said any of those things, you would actually have done the same things that the people who first came up with descriptive statistics said. They said, well, how can we do it? And we'll start by thinking of the idea of average. Average. And in everyday terminology, average has a very particular meaning. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
They said, well, how can we do it? And we'll start by thinking of the idea of average. Average. And in everyday terminology, average has a very particular meaning. As we'll see, when many people talk about average, they're talking about the arithmetic mean, which we'll see shortly. But in statistics, average means something more general. It really means give me a typical, give me a typical, or give me a middle, give me a middle number. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
And in everyday terminology, average has a very particular meaning. As we'll see, when many people talk about average, they're talking about the arithmetic mean, which we'll see shortly. But in statistics, average means something more general. It really means give me a typical, give me a typical, or give me a middle, give me a middle number. Or, and these are ors, and really, it's an attempt to find a measure of central tendency. Central, central tendency. So once again, you have a bunch of numbers. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
It really means give me a typical, give me a typical, or give me a middle, give me a middle number. Or, and these are ors, and really, it's an attempt to find a measure of central tendency. Central, central tendency. So once again, you have a bunch of numbers. You're somehow trying to represent these with one number. We'll call it the average. That's somehow typical or a middle or the center somehow of these numbers. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So once again, you have a bunch of numbers. You're somehow trying to represent these with one number. We'll call it the average. That's somehow typical or a middle or the center somehow of these numbers. And as we'll see, there's many types of averages. The first is the one that you're probably most familiar with. It's the one that people talk about, hey, the average on this exam or the average height. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
That's somehow typical or a middle or the center somehow of these numbers. And as we'll see, there's many types of averages. The first is the one that you're probably most familiar with. It's the one that people talk about, hey, the average on this exam or the average height. And that's the arithmetic mean. So let me write it in, I'll write it in yellow. Arith, arithmetic, arithmetic mean. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
It's the one that people talk about, hey, the average on this exam or the average height. And that's the arithmetic mean. So let me write it in, I'll write it in yellow. Arith, arithmetic, arithmetic mean. When arithmetic is a noun, we call it arithmetic. When it's an adjective like this, we call it arithmetic. Arithmetic mean. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Arith, arithmetic, arithmetic mean. When arithmetic is a noun, we call it arithmetic. When it's an adjective like this, we call it arithmetic. Arithmetic mean. And this is really just the sum of all the numbers divided by, and this is a human constructed definition that we've found useful, the sum of all of these numbers divided by the number of numbers we have. So given that, what is the arithmetic mean of this data set? Well, let's just compute it. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Arithmetic mean. And this is really just the sum of all the numbers divided by, and this is a human constructed definition that we've found useful, the sum of all of these numbers divided by the number of numbers we have. So given that, what is the arithmetic mean of this data set? Well, let's just compute it. It's going to be four plus three plus one plus six plus one plus seven over the number of data points we have. So we have six data points, so we're gonna divide by six. And we get four plus three is seven, plus one is eight, plus six is 14, plus one is 15, plus seven, 15 plus seven is 22. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Well, let's just compute it. It's going to be four plus three plus one plus six plus one plus seven over the number of data points we have. So we have six data points, so we're gonna divide by six. And we get four plus three is seven, plus one is eight, plus six is 14, plus one is 15, plus seven, 15 plus seven is 22. We'll do that one more time. You have seven, eight, 14, 15, 22. All of that over six. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
And we get four plus three is seven, plus one is eight, plus six is 14, plus one is 15, plus seven, 15 plus seven is 22. We'll do that one more time. You have seven, eight, 14, 15, 22. All of that over six. And we could write this as a mixed number. Six goes into 22 three times with the remainder of four. So it's three and 4 6, which is the same thing as three and 2 3rds. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
All of that over six. And we could write this as a mixed number. Six goes into 22 three times with the remainder of four. So it's three and 4 6, which is the same thing as three and 2 3rds. We could write this as a decimal with 3.6 repeating. So this is also 3.6 repeating. We could write it any one of those ways. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So it's three and 4 6, which is the same thing as three and 2 3rds. We could write this as a decimal with 3.6 repeating. So this is also 3.6 repeating. We could write it any one of those ways. But this is kind of a representative number. This is trying to get at a central tendency. Once again, these are human constructed. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
We could write it any one of those ways. But this is kind of a representative number. This is trying to get at a central tendency. Once again, these are human constructed. No one ever, it's not like someone just found some religious document that said, this is the way that the arithmetic mean must be defined. It's not as pure of a computation as say finding the circumference of the circle, which there really is. That was kind of, we studied the universe and that just fell out of our study of the universe. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Once again, these are human constructed. No one ever, it's not like someone just found some religious document that said, this is the way that the arithmetic mean must be defined. It's not as pure of a computation as say finding the circumference of the circle, which there really is. That was kind of, we studied the universe and that just fell out of our study of the universe. It's a human constructed definition that we found useful. Now, there are other ways to measure the average or find a typical or middle value. The other very typical way is the median. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
That was kind of, we studied the universe and that just fell out of our study of the universe. It's a human constructed definition that we found useful. Now, there are other ways to measure the average or find a typical or middle value. The other very typical way is the median. And I will write median, I'm running out of colors. I will write median in pink. So there is the median. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
The other very typical way is the median. And I will write median, I'm running out of colors. I will write median in pink. So there is the median. And the median is literally looking for the middle number. So if you were to order all the numbers in your set and find the middle one, then that is your median. So given that, what's the median of this set of numbers going to be? | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So there is the median. And the median is literally looking for the middle number. So if you were to order all the numbers in your set and find the middle one, then that is your median. So given that, what's the median of this set of numbers going to be? Let's try to figure it out. Let's try to order it. So we have one, then we have another one, then we have a three, then we have a four, a six and a seven. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So given that, what's the median of this set of numbers going to be? Let's try to figure it out. Let's try to order it. So we have one, then we have another one, then we have a three, then we have a four, a six and a seven. So all I did is I reordered this. And so what's the middle number? Well, you look here, since we have an even number of numbers we have six numbers. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So we have one, then we have another one, then we have a three, then we have a four, a six and a seven. So all I did is I reordered this. And so what's the middle number? Well, you look here, since we have an even number of numbers we have six numbers. There's not one middle number. You actually have two middle numbers here. You have two middle numbers right over here. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Well, you look here, since we have an even number of numbers we have six numbers. There's not one middle number. You actually have two middle numbers here. You have two middle numbers right over here. You have the three and the four. And in this case, when you have two middle numbers, you actually go halfway between these two numbers. Or essentially, you're taking the arithmetic mean of these two numbers to find the median. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
You have two middle numbers right over here. You have the three and the four. And in this case, when you have two middle numbers, you actually go halfway between these two numbers. Or essentially, you're taking the arithmetic mean of these two numbers to find the median. So the median is going to be halfway in between three and four which is going to be 3.5. So the median in this case is 3.5. So if you have an even number of numbers, the median or the middle two, essentially the arithmetic mean of the middle two are halfway between the middle two. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Or essentially, you're taking the arithmetic mean of these two numbers to find the median. So the median is going to be halfway in between three and four which is going to be 3.5. So the median in this case is 3.5. So if you have an even number of numbers, the median or the middle two, essentially the arithmetic mean of the middle two are halfway between the middle two. If you have an odd number of numbers, it's a little bit easier to compute. And just so that we see that, let me give you another data set. Let's say our data set, and I'll order it for us. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So if you have an even number of numbers, the median or the middle two, essentially the arithmetic mean of the middle two are halfway between the middle two. If you have an odd number of numbers, it's a little bit easier to compute. And just so that we see that, let me give you another data set. Let's say our data set, and I'll order it for us. Let's say our data set was 0,750, I don't know, 10,000, 10,000, and 1,000,000. 1,000,000. Let's say that that is our data set. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Let's say our data set, and I'll order it for us. Let's say our data set was 0,750, I don't know, 10,000, 10,000, and 1,000,000. 1,000,000. Let's say that that is our data set. Kind of a crazy data set. But in this situation, what is our median? Well, here we have five numbers. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Let's say that that is our data set. Kind of a crazy data set. But in this situation, what is our median? Well, here we have five numbers. We have an odd number of numbers. So it's easier to pick out a middle. The middle is a number that is greater than two of the numbers and is less than two of the numbers. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Well, here we have five numbers. We have an odd number of numbers. So it's easier to pick out a middle. The middle is a number that is greater than two of the numbers and is less than two of the numbers. It's exactly in the middle. So in this case, our median is 50. Now, the third measure of central tendency, and this is the one that's probably used least often in life, is the mode. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
The middle is a number that is greater than two of the numbers and is less than two of the numbers. It's exactly in the middle. So in this case, our median is 50. Now, the third measure of central tendency, and this is the one that's probably used least often in life, is the mode. And people often forget about it and it sounds like something very complex. But what we'll see is it's actually a very straightforward idea. And in some ways, it is the most basic idea. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Now, the third measure of central tendency, and this is the one that's probably used least often in life, is the mode. And people often forget about it and it sounds like something very complex. But what we'll see is it's actually a very straightforward idea. And in some ways, it is the most basic idea. So the mode is actually the most common number in a data set, if there is a most common number. If all the numbers are represented equally, if there's no one single most common number, then you have no mode. But given that definition of the mode, what is the single most common number in our original data set, in this data set right over here? | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
And in some ways, it is the most basic idea. So the mode is actually the most common number in a data set, if there is a most common number. If all the numbers are represented equally, if there's no one single most common number, then you have no mode. But given that definition of the mode, what is the single most common number in our original data set, in this data set right over here? Well, we only have one four. We only have one three. But we have two ones. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
But given that definition of the mode, what is the single most common number in our original data set, in this data set right over here? Well, we only have one four. We only have one three. But we have two ones. We have one six and one seven. So the number that shows up the most number of times here is our one. So the mode, the most typical number, the most common number here is a one. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
But we have two ones. We have one six and one seven. So the number that shows up the most number of times here is our one. So the mode, the most typical number, the most common number here is a one. So you see, these are all different ways of trying to get at a typical or middle or central tendency. But you do it in very, very different ways. And as we study more and more statistics, we'll see that they're good for different things. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
So the mode, the most typical number, the most common number here is a one. So you see, these are all different ways of trying to get at a typical or middle or central tendency. But you do it in very, very different ways. And as we study more and more statistics, we'll see that they're good for different things. This is used very frequently. The median is really good if you have some kind of crazy number out here that could have otherwise skewed the arithmetic mean. The mode could also be useful in situations like that, especially if you do have one number that's showing up a lot more frequently. | Statistics intro Mean, median, and mode Data and statistics 6th grade Khan Academy.mp3 |
Each dot plot below represents a different set of data. We see that here. Order the dot plots from largest standard deviation top to smallest standard deviation bottom. So pause this video and see if you can do that, or at least if you could rank these from largest standard deviation to smallest standard deviation. All right, now let's work through this together. And I'm doing this on Khan Academy where I can move these around to order them. But let's just remind ourselves what the standard deviation is or how we can perceive it. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
So pause this video and see if you can do that, or at least if you could rank these from largest standard deviation to smallest standard deviation. All right, now let's work through this together. And I'm doing this on Khan Academy where I can move these around to order them. But let's just remind ourselves what the standard deviation is or how we can perceive it. You could view the standard deviation as a measure of the typical distance from each of the data points to the mean. So the largest standard deviation, which we wanna put on top, would be the one where typically our data points are further from the mean and our smallest standard deviation would be the ones where it feels like, on average, our data points are closer to the mean. When all of these examples, our mean looks to be right in the center, right between 50 and 100, so right around 75. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
But let's just remind ourselves what the standard deviation is or how we can perceive it. You could view the standard deviation as a measure of the typical distance from each of the data points to the mean. So the largest standard deviation, which we wanna put on top, would be the one where typically our data points are further from the mean and our smallest standard deviation would be the ones where it feels like, on average, our data points are closer to the mean. When all of these examples, our mean looks to be right in the center, right between 50 and 100, so right around 75. So it's really about how spread apart they are from that. And if you look at this first one, it has these two data points, the one on the left and one on the right, that are pretty far, and then you have these two that are a little bit closer and then these two that are inside. This one right over here, to get from this top one to this middle one, you essentially are taking this data point and making it go further, and taking this data point and making it go further. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
When all of these examples, our mean looks to be right in the center, right between 50 and 100, so right around 75. So it's really about how spread apart they are from that. And if you look at this first one, it has these two data points, the one on the left and one on the right, that are pretty far, and then you have these two that are a little bit closer and then these two that are inside. This one right over here, to get from this top one to this middle one, you essentially are taking this data point and making it go further, and taking this data point and making it go further. And so this one is going to have a higher standard deviation than that one. So let me put it just like that. And I just wanna make it very clear. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
This one right over here, to get from this top one to this middle one, you essentially are taking this data point and making it go further, and taking this data point and making it go further. And so this one is going to have a higher standard deviation than that one. So let me put it just like that. And I just wanna make it very clear. Keep track of what's the difference between these two things. Here you have this data point and this data point that was closer in, and then if you move it further, that's going to make your typical distance from the middle more, which is exactly what happened there. Now what about this one? | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
And I just wanna make it very clear. Keep track of what's the difference between these two things. Here you have this data point and this data point that was closer in, and then if you move it further, that's going to make your typical distance from the middle more, which is exactly what happened there. Now what about this one? Well, this one is starting here and then taking this point and taking this point and moving it closer. And so that would make our typical distance from the middle, from the mean, shorter. So this would have the smallest standard deviation and this would have the largest. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
Now what about this one? Well, this one is starting here and then taking this point and taking this point and moving it closer. And so that would make our typical distance from the middle, from the mean, shorter. So this would have the smallest standard deviation and this would have the largest. Let's do another example. So same idea, order the dot plots from largest standard deviation on the top to smallest standard deviation on the bottom. Pause this video and see if you can figure that out. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
So this would have the smallest standard deviation and this would have the largest. Let's do another example. So same idea, order the dot plots from largest standard deviation on the top to smallest standard deviation on the bottom. Pause this video and see if you can figure that out. So this is interesting because these all have different means. Just eyeballing it, the mean for this first one is right around here. The mean for the second one is right around here at around 10. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
Pause this video and see if you can figure that out. So this is interesting because these all have different means. Just eyeballing it, the mean for this first one is right around here. The mean for the second one is right around here at around 10. And the mean for the third one, it looks like the same mean as this top one. And so pause this video. How would you order them? | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
The mean for the second one is right around here at around 10. And the mean for the third one, it looks like the same mean as this top one. And so pause this video. How would you order them? All right, so just eyeballing it, these, this middle one right over here, your typical data point seems furthest from the mean. You definitely have, if the mean is here, you have these, this data point and this data point that are quite far from that mean. And even this data point and this data point are at least as far as any of the data points that we have in the top or the bottom one. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
How would you order them? All right, so just eyeballing it, these, this middle one right over here, your typical data point seems furthest from the mean. You definitely have, if the mean is here, you have these, this data point and this data point that are quite far from that mean. And even this data point and this data point are at least as far as any of the data points that we have in the top or the bottom one. So I would say this has the largest standard deviation. And if I were to compare between these two, if you think about how you would get the difference between these two is if you took this data point and moved it at, and you moved it to the mean, and if you took this data point and you moved it to the mean, you would get this third situation. And so this third situation, you have the fewest data points that are sitting away from the mean relative to this one. | Visually assessing standard deviation AP Statistics Khan Academy.mp3 |
And in particular, I am going to put 8 green cubes. I'm also going to put some spheres in that bag. Let's say I'm going to put 9 spheres, and these are the green spheres. I'm also going to put some yellow cubes in that bag. Some yellow cubes. I'm going to put 5 of those. And I'm also going to put some yellow spheres in this bag. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I'm also going to put some yellow cubes in that bag. Some yellow cubes. I'm going to put 5 of those. And I'm also going to put some yellow spheres in this bag. Yellow spheres. And let's say I put 7 of those. I'm going to stick them all in this bag, and then I'm going to shake that bag, and then I'm going to pour it out, and I'm going to look at the first object that falls out of that bag. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And I'm also going to put some yellow spheres in this bag. Yellow spheres. And let's say I put 7 of those. I'm going to stick them all in this bag, and then I'm going to shake that bag, and then I'm going to pour it out, and I'm going to look at the first object that falls out of that bag. And what I want to think about in this video is what are the probabilities of getting different types of objects. So for example, what is the probability of getting a cube? A cube of any color. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I'm going to stick them all in this bag, and then I'm going to shake that bag, and then I'm going to pour it out, and I'm going to look at the first object that falls out of that bag. And what I want to think about in this video is what are the probabilities of getting different types of objects. So for example, what is the probability of getting a cube? A cube of any color. What is the probability of getting a cube? Well, to think about that, we should think about, or this is one way to think about it, what are all of the equally likely possibilities that might pop out of the bag? Well, we have 8 plus 9 is 17, 17 plus 5 is 22, 22 plus 7 is 29. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
A cube of any color. What is the probability of getting a cube? Well, to think about that, we should think about, or this is one way to think about it, what are all of the equally likely possibilities that might pop out of the bag? Well, we have 8 plus 9 is 17, 17 plus 5 is 22, 22 plus 7 is 29. So we have 29 objects. There are 29 objects in the bag. Did I do that right? | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Well, we have 8 plus 9 is 17, 17 plus 5 is 22, 22 plus 7 is 29. So we have 29 objects. There are 29 objects in the bag. Did I do that right? This is 14, yep, 29 objects. So let's draw all of the possible objects. And I'll represent it as this big area right over here. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Did I do that right? This is 14, yep, 29 objects. So let's draw all of the possible objects. And I'll represent it as this big area right over here. So these are all the possible objects. There are 29 possible objects. So there's 29 equal possibilities for the outcome of my experiment of seeing what pops out of that bag, assuming that it's equally likely for a cube or a sphere to pop out first. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And I'll represent it as this big area right over here. So these are all the possible objects. There are 29 possible objects. So there's 29 equal possibilities for the outcome of my experiment of seeing what pops out of that bag, assuming that it's equally likely for a cube or a sphere to pop out first. And how many of them meet our constraint of being a cube? Well, I have 8 green cubes, and I have 5 yellow cubes. So there are a total of 13 cubes. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So there's 29 equal possibilities for the outcome of my experiment of seeing what pops out of that bag, assuming that it's equally likely for a cube or a sphere to pop out first. And how many of them meet our constraint of being a cube? Well, I have 8 green cubes, and I have 5 yellow cubes. So there are a total of 13 cubes. So let me draw that set of cubes. So there's 13 cubes. I could draw it like this. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So there are a total of 13 cubes. So let me draw that set of cubes. So there's 13 cubes. I could draw it like this. There are 13 cubes. This right here is the set of cubes. This area, and I'm not drawing it exact, I'm approximating, represents the set of all the cubes. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I could draw it like this. There are 13 cubes. This right here is the set of cubes. This area, and I'm not drawing it exact, I'm approximating, represents the set of all the cubes. So the probability of getting a cube is the number of events that meet our criterion. So there's 13 possible cubes that have an equal likely chance of popping out over all of the possible equally likely events, which are 29. That includes the cubes and the spheres. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
This area, and I'm not drawing it exact, I'm approximating, represents the set of all the cubes. So the probability of getting a cube is the number of events that meet our criterion. So there's 13 possible cubes that have an equal likely chance of popping out over all of the possible equally likely events, which are 29. That includes the cubes and the spheres. Now let's ask a different question. What is the probability of getting a yellow object, either a cube or a sphere? So once again, how many things meet our conditions here? | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
That includes the cubes and the spheres. Now let's ask a different question. What is the probability of getting a yellow object, either a cube or a sphere? So once again, how many things meet our conditions here? We have 5 plus 7. There's 12 yellow objects in the bag. So we have 29 equally likely possibilities. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So once again, how many things meet our conditions here? We have 5 plus 7. There's 12 yellow objects in the bag. So we have 29 equally likely possibilities. I'll do that in the same color. We have 29 equally likely possibilities, and of those, 12 meet our criterion. So let me draw 12 right over here. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So we have 29 equally likely possibilities. I'll do that in the same color. We have 29 equally likely possibilities, and of those, 12 meet our criterion. So let me draw 12 right over here. I'll do my best attempt. It looks something like the set of yellow objects. There are 12 objects that are yellow. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So let me draw 12 right over here. I'll do my best attempt. It looks something like the set of yellow objects. There are 12 objects that are yellow. So the 12 that meet our conditions are 12 over all the possibilities, 29. So the probability of getting a cube, 13 29ths. Probability of getting a yellow, 12 29ths. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
There are 12 objects that are yellow. So the 12 that meet our conditions are 12 over all the possibilities, 29. So the probability of getting a cube, 13 29ths. Probability of getting a yellow, 12 29ths. Now let's ask something a little bit more interesting. What is the probability of getting a yellow cube? I'll put it in yellow, so we care about the color now. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Probability of getting a yellow, 12 29ths. Now let's ask something a little bit more interesting. What is the probability of getting a yellow cube? I'll put it in yellow, so we care about the color now. So this thing is yellow. What is the probability of getting a yellow cube? Well, there's 29 equally likely possibilities. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I'll put it in yellow, so we care about the color now. So this thing is yellow. What is the probability of getting a yellow cube? Well, there's 29 equally likely possibilities. And of those 29 equally likely possibilities, 5 of those are yellow cubes, or yellow cubes. 5 of them. So the probability is 5 29ths. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Well, there's 29 equally likely possibilities. And of those 29 equally likely possibilities, 5 of those are yellow cubes, or yellow cubes. 5 of them. So the probability is 5 29ths. And where would we see that on this Venn diagram that I've drawn? This is just a way to visualize the different probabilities. And they become interesting when you start thinking about where sets overlap, or even where they don't overlap. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So the probability is 5 29ths. And where would we see that on this Venn diagram that I've drawn? This is just a way to visualize the different probabilities. And they become interesting when you start thinking about where sets overlap, or even where they don't overlap. So here we're thinking about things that are members of the set yellow. So they're in this set, and they are cubes. So this area right over here, that's the overlap of these two sets. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And they become interesting when you start thinking about where sets overlap, or even where they don't overlap. So here we're thinking about things that are members of the set yellow. So they're in this set, and they are cubes. So this area right over here, that's the overlap of these two sets. So this area right over here, this represents things that are both yellow and cubes, because they are inside both circles. So this right over here, let me write it over here. So there's 5 objects that are both yellow and cubes. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So this area right over here, that's the overlap of these two sets. So this area right over here, this represents things that are both yellow and cubes, because they are inside both circles. So this right over here, let me write it over here. So there's 5 objects that are both yellow and cubes. Now let's ask, and this is probably the most interesting thing to ask, what is the probability of getting something that is yellow or a cube? A cube of any color. Well we still know that the denominator here is going to be 29. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So there's 5 objects that are both yellow and cubes. Now let's ask, and this is probably the most interesting thing to ask, what is the probability of getting something that is yellow or a cube? A cube of any color. Well we still know that the denominator here is going to be 29. These are all of the equally likely possibilities that might jump out of the bag. But what are the possibilities that meet our conditions? Well one way to think about it is, well there's 12 things that would meet the yellow condition. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Well we still know that the denominator here is going to be 29. These are all of the equally likely possibilities that might jump out of the bag. But what are the possibilities that meet our conditions? Well one way to think about it is, well there's 12 things that would meet the yellow condition. So that would be this entire circle right over here. 12 things that meet the yellow condition. So this right over here is 12. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Well one way to think about it is, well there's 12 things that would meet the yellow condition. So that would be this entire circle right over here. 12 things that meet the yellow condition. So this right over here is 12. This is the number of yellow, that is 12. And then to that, we can't just add the number of cubes, because if we add the number of cubes, we've already counted these 5. These 5 are counted as part of this 12. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So this right over here is 12. This is the number of yellow, that is 12. And then to that, we can't just add the number of cubes, because if we add the number of cubes, we've already counted these 5. These 5 are counted as part of this 12. One way to think about it is, there are 7 yellow objects that are not cubes. Those are the spheres. There are 5 yellow objects that are cubes. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
These 5 are counted as part of this 12. One way to think about it is, there are 7 yellow objects that are not cubes. Those are the spheres. There are 5 yellow objects that are cubes. And then there are 8 cubes that are not yellow. That's one way to think about it. So when we counted this 12, the number of yellow, we counted all of this. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
There are 5 yellow objects that are cubes. And then there are 8 cubes that are not yellow. That's one way to think about it. So when we counted this 12, the number of yellow, we counted all of this. So we can't just add the number of cubes to it, because then we would count this middle part again. So then we have to essentially count cubes, the number of cubes, which is 13. So number of cubes. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So when we counted this 12, the number of yellow, we counted all of this. So we can't just add the number of cubes to it, because then we would count this middle part again. So then we have to essentially count cubes, the number of cubes, which is 13. So number of cubes. And we'll have to subtract out this middle section right over here. Let me do this. So subtract out the middle section right over here. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So number of cubes. And we'll have to subtract out this middle section right over here. Let me do this. So subtract out the middle section right over here. So minus 5. So this is the number of yellow cubes. It feels weird to write the word yellow in green. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So subtract out the middle section right over here. So minus 5. So this is the number of yellow cubes. It feels weird to write the word yellow in green. The number of yellow cubes. Or another way to think about it, and you could just do this math right here, 12 plus 13 minus 5 is what? It's 20. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
It feels weird to write the word yellow in green. The number of yellow cubes. Or another way to think about it, and you could just do this math right here, 12 plus 13 minus 5 is what? It's 20. Did I do that right? 12 minus, yep, it's 20. So that's one way you just get this is equal to 20 over 29. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
It's 20. Did I do that right? 12 minus, yep, it's 20. So that's one way you just get this is equal to 20 over 29. But the more interesting thing than even the answer of the probability of getting that is expressing this in terms of the other probabilities that we figured out earlier in the video. So let's think about this a little bit. We can rewrite this fraction right over here. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So that's one way you just get this is equal to 20 over 29. But the more interesting thing than even the answer of the probability of getting that is expressing this in terms of the other probabilities that we figured out earlier in the video. So let's think about this a little bit. We can rewrite this fraction right over here. We can rewrite this as 12 over 29 plus 13 over 29 minus 5 over 29. And this was the number of yellow over the total possibilities. So this right over here was the probability of getting a yellow. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
We can rewrite this fraction right over here. We can rewrite this as 12 over 29 plus 13 over 29 minus 5 over 29. And this was the number of yellow over the total possibilities. So this right over here was the probability of getting a yellow. This right over here was the number of cubes over the total possibilities. So this is plus the probability of getting a cube. And this right over here was the number of yellow cubes over the total possibilities. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So this right over here was the probability of getting a yellow. This right over here was the number of cubes over the total possibilities. So this is plus the probability of getting a cube. And this right over here was the number of yellow cubes over the total possibilities. So this right over here was minus the probability of yellow and a cube. Let me write it that way. Minus the probability of yellow. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And this right over here was the number of yellow cubes over the total possibilities. So this right over here was minus the probability of yellow and a cube. Let me write it that way. Minus the probability of yellow. I'll write yellow in yellow. Yellow and getting a cube. And so what we've just done here, and you could play with the numbers, the numbers I just used as an example right here to make things a little bit concrete, but you can see this is a generalizable thing. | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
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