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Before, at the end of the last

video, I actually said that we'd talk about measures of

dispersion or how things are distributed, but before I go

into that, I realize that I have more to talk about,

especially the mean. And before I do that, I want

to differentiate between a sample and a population. I touched on this a little

bit in the last video. Let's say I wanted to

know — I don't know. Let's say I wanted to know

the average height of all men in America, right?

So let me make the set

of all men in America. So that's all men in America. I know there's 300 million

people in the U.S., and half of them maybe roughly are men,

so this would be 150 million men, right?

And it would be nearly

impossible, even if I was of every man in America. Frankly, you know, every few

seconds, one of these men is being born and one of

these men is dying. So you know by the time I'm

done measuring everything, someone would have died, and

some new men would have been born, so it would

almost be impossible. And if not impossible, it would

be very tiresome to measure the average, or the mean, or the

median, or the mode of this entire population, right?

So the best way I can get a

sense of this, because I'm interested in what the average

of the population is, maybe I can take the average

of a sample.

So what I could do is I can go

up to, you know — and I'd try to be pretty random about it. I don't want to like — you

know, hopefully, my sample wouldn't be my college's

basketball team because that would be a skewed sample, but

I'd try to find random people and random situations where it

wouldn't be skewed based on height.

And I'd maybe collect 10

heights, and I'd get, well, maybe — you know, the more

people I get the more indicative it is, but if I got

10 heights, and those 10

heights were — I don't know. I'll do it in, you know, 5

feet, 6 feet, 5 and a half feet, 5.75 feet, and, well,

let's say I only do 6, or let's say in 6 and

a half feet, right?

Those are the five people that

I'd sample, and we could talk more about what's a good way to

generate a random sample from a population so it's not skewed

one way or the other. But anyway, if I wanted to get

a sense of it and if I was kind of lazy, so I only took

five measurements, this is the way I would do it.

This would be a sample.

This would be a sample

of the population.

So instead of taking the mean —

let's say how I wanted to

calculate the average by

taking the arithmetic mean.

Instead of taking the

arithmetic mean of this entire group of 150 million people, I

might just be happy taking the mean of this sample, and

that'll be called the sample mean.

And I want to introduce you to

some notation, even though it's kind of — so in statistics

speak, the mean, this mu, it's

a Greek letter, essentially the

Greek letter that later turns into m, but mu is the

population mean, and this is just a convention

population mean.

And x with a line over it, that

is equal to a sample mean.

And these are just notations

that people might see, and you might have been confused

because sometimes you see something — people talk about

means, and you see this mu, and sometimes you see this x with a

line over it, and it's nice to know the distinction.

Here they're talking about

the mean of a sample of the population, and here they're

talking about the mean of the population as a whole. Now, the way you calculate

them is essentially the same.

video, I actually said that we'd talk about measures of

dispersion or how things are distributed, but before I go

into that, I realize that I have more to talk about,

especially the mean. And before I do that, I want

to differentiate between a sample and a population. I touched on this a little

bit in the last video. Let's say I wanted to

know — I don't know. Let's say I wanted to know

the average height of all men in America, right?

So let me make the set

of all men in America. So that's all men in America. I know there's 300 million

people in the U.S., and half of them maybe roughly are men,

so this would be 150 million men, right?

And it would be nearly

impossible, even if I was of every man in America. Frankly, you know, every few

seconds, one of these men is being born and one of

these men is dying. So you know by the time I'm

done measuring everything, someone would have died, and

some new men would have been born, so it would

almost be impossible. And if not impossible, it would

be very tiresome to measure the average, or the mean, or the

median, or the mode of this entire population, right?

So the best way I can get a

sense of this, because I'm interested in what the average

of the population is, maybe I can take the average

of a sample.

So what I could do is I can go

up to, you know — and I'd try to be pretty random about it. I don't want to like — you

know, hopefully, my sample wouldn't be my college's

basketball team because that would be a skewed sample, but

I'd try to find random people and random situations where it

wouldn't be skewed based on height.

And I'd maybe collect 10

heights, and I'd get, well, maybe — you know, the more

people I get the more indicative it is, but if I got

10 heights, and those 10

heights were — I don't know. I'll do it in, you know, 5

feet, 6 feet, 5 and a half feet, 5.75 feet, and, well,

let's say I only do 6, or let's say in 6 and

a half feet, right?

Those are the five people that

I'd sample, and we could talk more about what's a good way to

generate a random sample from a population so it's not skewed

one way or the other. But anyway, if I wanted to get

a sense of it and if I was kind of lazy, so I only took

five measurements, this is the way I would do it.

This would be a sample.

This would be a sample

of the population.

So instead of taking the mean —

let's say how I wanted to

calculate the average by

taking the arithmetic mean.

Instead of taking the

arithmetic mean of this entire group of 150 million people, I

might just be happy taking the mean of this sample, and

that'll be called the sample mean.

And I want to introduce you to

some notation, even though it's kind of — so in statistics

speak, the mean, this mu, it's

a Greek letter, essentially the

Greek letter that later turns into m, but mu is the

population mean, and this is just a convention

population mean.

And x with a line over it, that

is equal to a sample mean.

And these are just notations

that people might see, and you might have been confused

because sometimes you see something — people talk about

means, and you see this mu, and sometimes you see this x with a

line over it, and it's nice to know the distinction.

Here they're talking about

the mean of a sample of the population, and here they're

talking about the mean of the population as a whole. Now, the way you calculate

them is essentially the same.

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