Statistics: Sample vs. Population Mean Video2

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.