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The insurance company pays everything after that. So you could say 8,000 plus, there's a 70% chance that he's going to pay 1,000. And once again, this table is a pretty big simplification from the real world. There's probably a lot of scenarios where you'd have to pay $500 or $600 or whatever it might be. But let's just go with this. And so that's essentially a simplification. There's a 70% chance that he's going to have to pay $1,000. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
There's probably a lot of scenarios where you'd have to pay $500 or $600 or whatever it might be. But let's just go with this. And so that's essentially a simplification. There's a 70% chance that he's going to have to pay $1,000. And so that's $700 expected cost from that plus the 8,000 from the insurance gets us to $8,700. So let's write that down. So 8,700, my pen is really acting up. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
There's a 70% chance that he's going to have to pay $1,000. And so that's $700 expected cost from that plus the 8,000 from the insurance gets us to $8,700. So let's write that down. So 8,700, my pen is really acting up. I don't know what's going on here. I think I have to get a new tablet. You can't even read that. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
So 8,700, my pen is really acting up. I don't know what's going on here. I think I have to get a new tablet. You can't even read that. Let me write this. 87, whoops. $8,700, including the cost of insurance, what are Paul's expected total medical costs with the high deductible plan? | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
You can't even read that. Let me write this. 87, whoops. $8,700, including the cost of insurance, what are Paul's expected total medical costs with the high deductible plan? Round your answer to the nearest cent. So let's look at the high deductible plan. So he's going to pay 7,500 no matter what. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
$8,700, including the cost of insurance, what are Paul's expected total medical costs with the high deductible plan? Round your answer to the nearest cent. So let's look at the high deductible plan. So he's going to pay 7,500 no matter what. 7,500 no matter what. And then, so there's a zero, we could write $0 times 30% or 30% times $0, but that's just going to be zero. There's a 25% chance he spends $1,000. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
So he's going to pay 7,500 no matter what. 7,500 no matter what. And then, so there's a zero, we could write $0 times 30% or 30% times $0, but that's just going to be zero. There's a 25% chance he spends $1,000. So plus.25 times 1,000. There's a 20% chance plus.2. He's not going to spend 4,000 here. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
There's a 25% chance he spends $1,000. So plus.25 times 1,000. There's a 20% chance plus.2. He's not going to spend 4,000 here. He's going to have to spend the first 2,500. So it's a 20% chance he spends 2,500. So times 2,500, insurance company will pay the next 1,500, plus another 20% chance. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
He's not going to spend 4,000 here. He's going to have to spend the first 2,500. So it's a 20% chance he spends 2,500. So times 2,500, insurance company will pay the next 1,500, plus another 20% chance. Even in this situation, he only has to pay 2,500. So times 2,500. And then finally, plus, there's a 5% chance. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
So times 2,500, insurance company will pay the next 1,500, plus another 20% chance. Even in this situation, he only has to pay 2,500. So times 2,500. And then finally, plus, there's a 5% chance. Even in this situation, he only has to pay the first 2,500. Times 2,500 gets us to $8,875. $8,875. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
And then finally, plus, there's a 5% chance. Even in this situation, he only has to pay the first 2,500. Times 2,500 gets us to $8,875. $8,875. $8,875. And once again, you could think about it as, okay, there's a 25% chance that he pays 1,000, and then there is a 45% chance that he pays $2,500. All of these situations, he's paying $2,500. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
$8,875. $8,875. And once again, you could think about it as, okay, there's a 25% chance that he pays 1,000, and then there is a 45% chance that he pays $2,500. All of these situations, he's paying $2,500. But either way, you would get $8,875. If Paul wants the best payoff in the long run and must buy one of the two insurance plans, he should purchase the, well, his expected total cost of medical, cost of insurance, including medical costs, is lower with the low deductible plan. So this one, he should go with the low, low deductible. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
All of these situations, he's paying $2,500. But either way, you would get $8,875. If Paul wants the best payoff in the long run and must buy one of the two insurance plans, he should purchase the, well, his expected total cost of medical, cost of insurance, including medical costs, is lower with the low deductible plan. So this one, he should go with the low, low deductible. Low deductible. Which, once again, you shouldn't use these videos as kind of insurance advice. This is actually, but also, it's an interesting way to think about it. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
So this one, he should go with the low, low deductible. Low deductible. Which, once again, you shouldn't use these videos as kind of insurance advice. This is actually, but also, it's an interesting way to think about it. It's typically, well, it's not always typically the case that the low deductible plan is going to have a higher long-term, or the low deductible plan is going to be a better deal. It's usually the, well, I won't make any actuarial statements but at least in this situation, the low deductible plan seems like the better deal. It's lower expected total cost given these probabilities. | Comparing insurance with expected value Probability and Statistics Khan Academy.mp3 |
So over this axis right over here, the horizontal axis, they have month by month, and we move forward in time, July, August, September, October. And in this axis, the vertical axis, we have the price. So for example, in July, the price of this stock was a little over $10. Then in August, it moved up to, it looks like, around $11. And then we could keep going month by month. And this type of graph right over here is called a line graph because you have the data points for each month. And then we connected them with a line. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Then in August, it moved up to, it looks like, around $11. And then we could keep going month by month. And this type of graph right over here is called a line graph because you have the data points for each month. And then we connected them with a line. And the reason why we connect them with a line is to really see if there's some kind of a trend here, to really show that you have something that's moving from one price to another. And so line graphs tend to be used when you have something that's changing over time. Now with that out of the way, let's actually answer their question. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And then we connected them with a line. And the reason why we connect them with a line is to really see if there's some kind of a trend here, to really show that you have something that's moving from one price to another. And so line graphs tend to be used when you have something that's changing over time. Now with that out of the way, let's actually answer their question. Over the course of the year, is the price of the stock rising, falling, or staying the same? So on a month-to-month basis, you have, for example, from July to August, the price went up. Then from August to September, the price went down. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Now with that out of the way, let's actually answer their question. Over the course of the year, is the price of the stock rising, falling, or staying the same? So on a month-to-month basis, you have, for example, from July to August, the price went up. Then from August to September, the price went down. Then it went up for two months. Then it went down for a month. Then it went up for a couple of more months. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Then from August to September, the price went down. Then it went up for two months. Then it went down for a month. Then it went up for a couple of more months. Then it went really up from February to March, went all the way up to almost $17. Then it went down again. And then it kept going up again. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Then it went up for a couple of more months. Then it went really up from February to March, went all the way up to almost $17. Then it went down again. And then it kept going up again. But they're asking us not, you know, did it go up every month? They're saying over the course of the year. Over the course of the year, is the price of the stock rising, falling, or staying the same? | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And then it kept going up again. But they're asking us not, you know, did it go up every month? They're saying over the course of the year. Over the course of the year, is the price of the stock rising, falling, or staying the same? And if you go from July, which is where our data starts right over here, our price was around $10. And even though there were a few months where it went down, the overall trend is that the price is going up. The overall trend is that the price is going up. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
Over the course of the year, is the price of the stock rising, falling, or staying the same? And if you go from July, which is where our data starts right over here, our price was around $10. And even though there were a few months where it went down, the overall trend is that the price is going up. The overall trend is that the price is going up. And you can even see that. In July, it was $10. And then by June of the next year, it was approaching, I don't know, it looks like it's about almost a little over $16, maybe almost $17. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
The overall trend is that the price is going up. And you can even see that. In July, it was $10. And then by June of the next year, it was approaching, I don't know, it looks like it's about almost a little over $16, maybe almost $17. So it actually had gone up a lot. They don't give us July of the next year, but the overall trend is definitely the upwards direction right over here. And you can see it just visually by looking at this line graph. | Reading line graphs Applying mathematical reasoning Pre-Algebra Khan Academy.mp3 |
And statistics is really a broad category of things that you might do with data. So it generally deals with data, collecting data. So actually let me write these down. It's involving collecting data. Collecting data. You could present data in tables or charts or just as lists of numbers or however you might do it. It is analyzing the data. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
It's involving collecting data. Collecting data. You could present data in tables or charts or just as lists of numbers or however you might do it. It is analyzing the data. Analyzing, analyzing, presenting and analyzing data. So this whole class of just, you know, all the stuff that you might do with data to answer a question or try to figure out what's going on or just to learn about the world, that whole class of things is called statistics. Now an idea that will come up very frequently in statistics is the notion of variability. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
It is analyzing the data. Analyzing, analyzing, presenting and analyzing data. So this whole class of just, you know, all the stuff that you might do with data to answer a question or try to figure out what's going on or just to learn about the world, that whole class of things is called statistics. Now an idea that will come up very frequently in statistics is the notion of variability. Variability. In everyday language, variability, it's how much something is, how much does it vary? How much does it change? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Now an idea that will come up very frequently in statistics is the notion of variability. Variability. In everyday language, variability, it's how much something is, how much does it vary? How much does it change? And it's the same notion in statistics. In statistics, variability is the degree to which data points are different from each other, the degree to which they vary. And just as an example of that, to just make it a little bit more concrete, let's say you were to go to five people and you were to ask them, how many bricks did you eat yesterday? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
How much does it change? And it's the same notion in statistics. In statistics, variability is the degree to which data points are different from each other, the degree to which they vary. And just as an example of that, to just make it a little bit more concrete, let's say you were to go to five people and you were to ask them, how many bricks did you eat yesterday? And each of the people say, well, you know, a person once said, I don't eat bricks at all. I don't even know how to do that. I ate zero bricks. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
And just as an example of that, to just make it a little bit more concrete, let's say you were to go to five people and you were to ask them, how many bricks did you eat yesterday? And each of the people say, well, you know, a person once said, I don't eat bricks at all. I don't even know how to do that. I ate zero bricks. And then the next person says zero, the next person says zero, fourth person says zero, and the fifth person says zero. Fair enough, so that was our data point on the different data points on, and I'm already doing statistics just by going out there and asking them how many bricks they ate. Then I ask them, how many grapes did you eat yesterday? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
I ate zero bricks. And then the next person says zero, the next person says zero, fourth person says zero, and the fifth person says zero. Fair enough, so that was our data point on the different data points on, and I'm already doing statistics just by going out there and asking them how many bricks they ate. Then I ask them, how many grapes did you eat yesterday? And the first person says, I ate zero grapes, but the next person says, I survive on grapes. I ate 235 grapes. The next person says, yeah, I like grapes. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Then I ask them, how many grapes did you eat yesterday? And the first person says, I ate zero grapes, but the next person says, I survive on grapes. I ate 235 grapes. The next person says, yeah, I like grapes. I ate 17 grapes. Then the person after that says that they ate five grapes. And then the next person also survives on grapes, even to a larger degree. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
The next person says, yeah, I like grapes. I ate 17 grapes. Then the person after that says that they ate five grapes. And then the next person also survives on grapes, even to a larger degree. They ate 318 grapes. So if you look at these two data sets, one is the number of bricks someone ate yesterday, the other one is how many grapes they ate yesterday, you immediately see that there's more variability here. All of these data points are zero, while these, they change a good bit from data point to data point. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
And then the next person also survives on grapes, even to a larger degree. They ate 318 grapes. So if you look at these two data sets, one is the number of bricks someone ate yesterday, the other one is how many grapes they ate yesterday, you immediately see that there's more variability here. All of these data points are zero, while these, they change a good bit from data point to data point. So we have a sense that there is more variability in this data set. Now one of the things we will start doing a lot in statistics is trying to measure how much more, how much variability is, how can we quantify that? How can we put a number on it? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
All of these data points are zero, while these, they change a good bit from data point to data point. So we have a sense that there is more variability in this data set. Now one of the things we will start doing a lot in statistics is trying to measure how much more, how much variability is, how can we quantify that? How can we put a number on it? How can we measure variability? This is a big aspect of statistics, but we won't do that in this video. There are future videos for doing that. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
How can we put a number on it? How can we measure variability? This is a big aspect of statistics, but we won't do that in this video. There are future videos for doing that. But just as we go into the world of statistics, we should think about, well, when do we even, when should our brain even start getting into statistics mode? Thinking about the tools that we have at our disposal, about collecting data and measuring variability and measuring and finding numbers that somehow represent a data, a pool of data that has variability. And so the question we should ask ourselves is, what questions in the world are statistical questions? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
There are future videos for doing that. But just as we go into the world of statistics, we should think about, well, when do we even, when should our brain even start getting into statistics mode? Thinking about the tools that we have at our disposal, about collecting data and measuring variability and measuring and finding numbers that somehow represent a data, a pool of data that has variability. And so the question we should ask ourselves is, what questions in the world are statistical questions? So statistical, statistical questions. So let's come up with a definition for statistical question, the type of question where we would want to start bringing out our statistical, our statistical toolkit. Well, one possible way to think about when you need to bring out your statistical toolkit is these are questions that to answer them, to answer, you need to collect data with variability. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
And so the question we should ask ourselves is, what questions in the world are statistical questions? So statistical, statistical questions. So let's come up with a definition for statistical question, the type of question where we would want to start bringing out our statistical, our statistical toolkit. Well, one possible way to think about when you need to bring out your statistical toolkit is these are questions that to answer them, to answer, you need to collect data with variability. To answer, you need to collect data with variability. And apologize for my handwriting. Data with variability. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Well, one possible way to think about when you need to bring out your statistical toolkit is these are questions that to answer them, to answer, you need to collect data with variability. To answer, you need to collect data with variability. And apologize for my handwriting. Data with variability. That's W-I-T-H, data with variability. Variability. So you're saying, okay, that kind of makes sense, but I need to see some tangible questions, or tangible examples of things that are statistical questions and things that are not statistical questions. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Data with variability. That's W-I-T-H, data with variability. Variability. So you're saying, okay, that kind of makes sense, but I need to see some tangible questions, or tangible examples of things that are statistical questions and things that are not statistical questions. And I would say, fair enough, let's look at some examples. So here I have six questions, and I encourage you to pause this video right now, and before I work through it, think about it. Based on this definition of a statistical question, which of these questions are statistical, would require your kind of statistical toolkit, and which of these are not statistical? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
So you're saying, okay, that kind of makes sense, but I need to see some tangible questions, or tangible examples of things that are statistical questions and things that are not statistical questions. And I would say, fair enough, let's look at some examples. So here I have six questions, and I encourage you to pause this video right now, and before I work through it, think about it. Based on this definition of a statistical question, which of these questions are statistical, would require your kind of statistical toolkit, and which of these are not statistical? So I'm assuming you've had a go at it. Let's go through these one by one. So the first question, how much does my pet grapefruit weigh? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Based on this definition of a statistical question, which of these questions are statistical, would require your kind of statistical toolkit, and which of these are not statistical? So I'm assuming you've had a go at it. Let's go through these one by one. So the first question, how much does my pet grapefruit weigh? Now, it's bizarre to begin with to have a pet grapefruit, but is this a statistical question? Well, what do I need to do to answer it? I have to take my pet grapefruit out, I have to weigh it, and then I have to just write that down. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
So the first question, how much does my pet grapefruit weigh? Now, it's bizarre to begin with to have a pet grapefruit, but is this a statistical question? Well, what do I need to do to answer it? I have to take my pet grapefruit out, I have to weigh it, and then I have to just write that down. And just doing that, I am collecting data, so you could argue that maybe I'm kinda starting to mess with statistics a little bit, but I'm just getting one data point. So I might weigh it, and I might see my grapefruit weighs one pound, but that's not data with variability, that's just one data point. In order to have variability, I have to have multiple data points, and it should be at least possible that they could vary. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
I have to take my pet grapefruit out, I have to weigh it, and then I have to just write that down. And just doing that, I am collecting data, so you could argue that maybe I'm kinda starting to mess with statistics a little bit, but I'm just getting one data point. So I might weigh it, and I might see my grapefruit weighs one pound, but that's not data with variability, that's just one data point. In order to have variability, I have to have multiple data points, and it should be at least possible that they could vary. So for example, all of these folks ate zero bricks, and maybe it was possible that someone actually ate a brick. But here I just have one data point. With one data point, you can't have variability. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
In order to have variability, I have to have multiple data points, and it should be at least possible that they could vary. So for example, all of these folks ate zero bricks, and maybe it was possible that someone actually ate a brick. But here I just have one data point. With one data point, you can't have variability. So this is not a statistical question. I just collect a data point. Next question, what is the average number of cars in a parking lot on Monday mornings? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
With one data point, you can't have variability. So this is not a statistical question. I just collect a data point. Next question, what is the average number of cars in a parking lot on Monday mornings? Well, to think about whether it is a statistical question, we just have to think about what do I have to do to answer that question? Well, I would have to go out to the parking lot on multiple Monday mornings and measure the number of cars. So on the first Monday morning, I might see there are 50 cars. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Next question, what is the average number of cars in a parking lot on Monday mornings? Well, to think about whether it is a statistical question, we just have to think about what do I have to do to answer that question? Well, I would have to go out to the parking lot on multiple Monday mornings and measure the number of cars. So on the first Monday morning, I might see there are 50 cars. The next Monday morning, I might go out there and count, there's 49 cars. The next Monday morning, I might see 50 cars again. The next Monday morning, I might see 63 cars. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
So on the first Monday morning, I might see there are 50 cars. The next Monday morning, I might go out there and count, there's 49 cars. The next Monday morning, I might see 50 cars again. The next Monday morning, I might see 63 cars. So I'm collecting multiple data points to answer this question. Then I'm gonna take the average of all of these, but I'm collecting multiple data points to answer this question. And it's definitely possible that there could be variation here, that there could be variability. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
The next Monday morning, I might see 63 cars. So I'm collecting multiple data points to answer this question. Then I'm gonna take the average of all of these, but I'm collecting multiple data points to answer this question. And it's definitely possible that there could be variation here, that there could be variability. So this is a statistical question. Next question, am I hungry? It's an important question. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
And it's definitely possible that there could be variation here, that there could be variability. So this is a statistical question. Next question, am I hungry? It's an important question. We need to ask it to ourselves multiple times. In fact, sometimes our bodies just tell it to us. But I am definitely not collecting, I guess you could say I'm collecting some type of feelings from my stomach or how weak I feel or not. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
It's an important question. We need to ask it to ourselves multiple times. In fact, sometimes our bodies just tell it to us. But I am definitely not collecting, I guess you could say I'm collecting some type of feelings from my stomach or how weak I feel or not. But it's definitely not data with variability. I'm either hungry or not hungry on a given day. I mean, if you said broader, how does my hunger change from day to day, and you came up with some type of a scale for rating your hunger, okay, maybe that's more statistical. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
But I am definitely not collecting, I guess you could say I'm collecting some type of feelings from my stomach or how weak I feel or not. But it's definitely not data with variability. I'm either hungry or not hungry on a given day. I mean, if you said broader, how does my hunger change from day to day, and you came up with some type of a scale for rating your hunger, okay, maybe that's more statistical. But just am I hungry, a yes, no question, this is not, to answer this, I do not have to collect data with variability. So this is not a statistical question. How many teeth does my mother have? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
I mean, if you said broader, how does my hunger change from day to day, and you came up with some type of a scale for rating your hunger, okay, maybe that's more statistical. But just am I hungry, a yes, no question, this is not, to answer this, I do not have to collect data with variability. So this is not a statistical question. How many teeth does my mother have? To do this, I would have to go find my mother, and then I would have to ask her to open her mouth and count the teeth in her mouth. And maybe I get a number like 30. So it's kind of like how much does my pet grapefruit weigh? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
How many teeth does my mother have? To do this, I would have to go find my mother, and then I would have to ask her to open her mouth and count the teeth in her mouth. And maybe I get a number like 30. So it's kind of like how much does my pet grapefruit weigh? I do have to collect one data point, but one data point is not going to have variability. So I am not collecting data with variability. So this is not a statistical question. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
So it's kind of like how much does my pet grapefruit weigh? I do have to collect one data point, but one data point is not going to have variability. So I am not collecting data with variability. So this is not a statistical question. If I said how many teeth do all of the mothers that I know have on average, or what's the range of number of teeth that the mothers I know have, well, that would start getting, or that would be statistical. But this is just one data point, so not statistical. How much time do the members of my family spend eating per year? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
So this is not a statistical question. If I said how many teeth do all of the mothers that I know have on average, or what's the range of number of teeth that the mothers I know have, well, that would start getting, or that would be statistical. But this is just one data point, so not statistical. How much time do the members of my family spend eating per year? Well, once again, what do I need to do to answer this question? Well, I would have to go either observe or survey my family members, maybe my mom, my wife, my children, and my uncles, aunts, whoever else. I would say, well, how much do you eat each day? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
How much time do the members of my family spend eating per year? Well, once again, what do I need to do to answer this question? Well, I would have to go either observe or survey my family members, maybe my mom, my wife, my children, and my uncles, aunts, whoever else. I would say, well, how much do you eat each day? I would add them all up to figure out how much they eat in the year. And maybe family member A eats 813 hours in a year. Family member B ate, I don't know, 732 hours in the year. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
I would say, well, how much do you eat each day? I would add them all up to figure out how much they eat in the year. And maybe family member A eats 813 hours in a year. Family member B ate, I don't know, 732 hours in the year. And so you see the general notion that I will be collecting multiple data points from the different family members, and they're very well, and in fact, there's very likely to be variation in that. In fact, I might even see variation from year to year. Person A is probably going to need a different number of hours in the next year. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Family member B ate, I don't know, 732 hours in the year. And so you see the general notion that I will be collecting multiple data points from the different family members, and they're very well, and in fact, there's very likely to be variation in that. In fact, I might even see variation from year to year. Person A is probably going to need a different number of hours in the next year. So I'm definitely going to collect data with variability in order to answer this question. So that is a statistical question. And then finally, I have the question, how many times have I watched Star Wars? | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
Person A is probably going to need a different number of hours in the next year. So I'm definitely going to collect data with variability in order to answer this question. So that is a statistical question. And then finally, I have the question, how many times have I watched Star Wars? Well, this is very similar to how many teeth does my mother have, or how much does my pet grapefruit weigh. I just have to count the number of times that I watched Star Wars, and maybe, you know, I watched it seven times, just one data point. No variability here. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
And then finally, I have the question, how many times have I watched Star Wars? Well, this is very similar to how many teeth does my mother have, or how much does my pet grapefruit weigh. I just have to count the number of times that I watched Star Wars, and maybe, you know, I watched it seven times, just one data point. No variability here. If I said, on average, how many times have my coworkers watched Star Wars? Well, then I'm going to have to collect data with variability. I'm gonna collect multiple data points, and it's definitely possible that my coworkers have watched it different numbers of times. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
No variability here. If I said, on average, how many times have my coworkers watched Star Wars? Well, then I'm going to have to collect data with variability. I'm gonna collect multiple data points, and it's definitely possible that my coworkers have watched it different numbers of times. But for this question in particular, where it's just one data point to answer it, how many times have I watched Star Wars? And my answer in this case, actually, I think is seven. Well, then not a statistical question. | Statistical questions Data and statistics 6th grade Khan Academy.mp3 |
You can see there's seven equally likely possibilities. Let's see, there's one, two, three, four, five, six, seven equally likely possibilities. It looks like in four of them you've spun an elephant. Two of them you have this mouse running away from something. And then in one of them you have this monkey doing some type of acrobatics. Fair enough. Now let's pose ourselves an interesting question. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
Two of them you have this mouse running away from something. And then in one of them you have this monkey doing some type of acrobatics. Fair enough. Now let's pose ourselves an interesting question. At least I think it's an interesting question. Let's say we were to spin this spinner 210 times. So we're gonna spin 210, we're gonna spin that spinner 210 times. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
Now let's pose ourselves an interesting question. At least I think it's an interesting question. Let's say we were to spin this spinner 210 times. So we're gonna spin 210, we're gonna spin that spinner 210 times. And I want you to make a prediction. I want you to predict, I want you to predict the number of times, the number of times we get an elephant. We get an elephant. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
So we're gonna spin 210, we're gonna spin that spinner 210 times. And I want you to make a prediction. I want you to predict, I want you to predict the number of times, the number of times we get an elephant. We get an elephant. Number of times we get an elephant out of the 210 times. So why don't you have a go at it. Alright, so I'm assuming like always pause the video and had a try. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
We get an elephant. Number of times we get an elephant out of the 210 times. So why don't you have a go at it. Alright, so I'm assuming like always pause the video and had a try. So one way to think about it is, well for one spin what is the probability of getting an elephant? So let's do this. One spin, so for one spin what is the probability of getting an elephant? | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
Alright, so I'm assuming like always pause the video and had a try. So one way to think about it is, well for one spin what is the probability of getting an elephant? So let's do this. One spin, so for one spin what is the probability of getting an elephant? Well let's see, we have already talked about this is a fair spinner. There's seven equally likely possibilities. And then how many involve getting an elephant? | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
One spin, so for one spin what is the probability of getting an elephant? Well let's see, we have already talked about this is a fair spinner. There's seven equally likely possibilities. And then how many involve getting an elephant? Well so we have one, two, three, four. Four out of the seven equally likely possibilities involve us getting an elephant. So one reasonable thing to do, and this is actually what I would do, is let's go look. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
And then how many involve getting an elephant? Well so we have one, two, three, four. Four out of the seven equally likely possibilities involve us getting an elephant. So one reasonable thing to do, and this is actually what I would do, is let's go look. Four sevenths probability means I should expect that four sevenths of the time, especially if I'm doing a lot of these, if I'm doing it over and over and over again, it's a reasonable expectation that, hey, four sevenths of the time I will get an elephant. I've just calculated the theoretical probability here based on this being a fair spinner. And that should inform that if I were to do a bunch of experiments that four sevenths of the time that I should see me getting the elephant. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
So one reasonable thing to do, and this is actually what I would do, is let's go look. Four sevenths probability means I should expect that four sevenths of the time, especially if I'm doing a lot of these, if I'm doing it over and over and over again, it's a reasonable expectation that, hey, four sevenths of the time I will get an elephant. I've just calculated the theoretical probability here based on this being a fair spinner. And that should inform that if I were to do a bunch of experiments that four sevenths of the time that I should see me getting the elephant. So it would be a reasonable prediction to say, look, I'm gonna spin this thing 210 times, and I would expect that four sevenths of those 210 times I would get an elephant. And so let's think about what this is. 210 times four sevenths, 210 divided by seven is 30, 30 times 40 is 120. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
And that should inform that if I were to do a bunch of experiments that four sevenths of the time that I should see me getting the elephant. So it would be a reasonable prediction to say, look, I'm gonna spin this thing 210 times, and I would expect that four sevenths of those 210 times I would get an elephant. And so let's think about what this is. 210 times four sevenths, 210 divided by seven is 30, 30 times 40 is 120. So 120 times. My prediction, or maybe your prediction was this as well, I think it's a reasonable prediction, is that if I spin it 210 times, that I'm going to get an elephant 120 times. Now it's very important to think about what this is saying and this is not saying. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
210 times four sevenths, 210 divided by seven is 30, 30 times 40 is 120. So 120 times. My prediction, or maybe your prediction was this as well, I think it's a reasonable prediction, is that if I spin it 210 times, that I'm going to get an elephant 120 times. Now it's very important to think about what this is saying and this is not saying. Is it possible that I get an elephant 121 times, or maybe 119 times? Sure, sure, it's completely reasonable that you might get something different than this. In fact, there's some probability that you get no elephant. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
Now it's very important to think about what this is saying and this is not saying. Is it possible that I get an elephant 121 times, or maybe 119 times? Sure, sure, it's completely reasonable that you might get something different than this. In fact, there's some probability that you get no elephant. If you consider getting an elephant lucky, that you just happen to keep landing on the monkey or one of the mice. Now it's a very low probability that that would happen if you spun it 210 times, but it is possible. So it's important to realize that this is just a pretty, there's actually a possibility that you might get an elephant on all 210 spins. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
In fact, there's some probability that you get no elephant. If you consider getting an elephant lucky, that you just happen to keep landing on the monkey or one of the mice. Now it's a very low probability that that would happen if you spun it 210 times, but it is possible. So it's important to realize that this is just a pretty, there's actually a possibility that you might get an elephant on all 210 spins. Once again, that's a low probability, but it is possible. So this isn't saying that you're definitely going to get the elephant 120 times. In fact, it's very reasonable that you might get the elephant 123 times, or 128 times, or 110 times, or even 90 times. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
So it's important to realize that this is just a pretty, there's actually a possibility that you might get an elephant on all 210 spins. Once again, that's a low probability, but it is possible. So this isn't saying that you're definitely going to get the elephant 120 times. In fact, it's very reasonable that you might get the elephant 123 times, or 128 times, or 110 times, or even 90 times. These are all completely reasonable things to happen. All you would say is that, look, if I had to predict it, this, out of all of the different, I can get the elephant anywhere between zero and 210 times. Out of all of those possibilities, before I even start spinning, I'll say, okay, I think that this is the most reasonable one, that I'm going to get it 4 7ths of the time. | Making predictions with probability Statistics and probability 7th grade Khan Academy.mp3 |
In fact, it's very reasonable that you might get the elephant 123 times, or 128 times, or 110 times, or even 90 times. These are all completely reasonable things to happen. All you would say is that, look, if I had to predict it, this, out of all of the different, I can get the elephant anywhere between zero and 210 times. Out of all of those possibilities, before I even start spinning, I'll say, okay, I think that this is the most reasonable one, that I'm going to get it 4 7ths of the time. But it's not saying that, hey, yeah, it's not saying that I'm definitely going to get it 120 times. It's not saying that 118 times, or 129 times aren't reasonably possible as well. It's just saying, look, this is a reasonable prediction. | Making predictions with probability Statistics and probability 7th grade 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 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. | 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 even say the frequency. | 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 at that age. | 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, no eights, four nines, one 10, no 11s, and two 12s. And then you would just have this list of numbers. | 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 frequency table is a dot plot. So let me draw a dot plot right over here. So a dot plot. | 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, what we would have of, actually let me just not draw an even arrow there. We have the different age groups. | 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. 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. | 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-year-olds, so one, two, three, four dots. | 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 put a dot, one dot, right over there for that one 10-year-old. | 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 there's two 12-year-olds. So one 12-year-old and another 12-year-old. | Frequency tables and dot plots Data and statistics 6th grade Khan Academy.mp3 |
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