Now remember what we are originally trying to find. We're trying to find where
on the distribution of sample means a particular sample will lie. Not just for a
simple population like this one, but for a huge population. And now we can do
that. Because now we know that the distribution of means, where every mean is
the mean of a sample of size n. This distribution has a standard deviation equal
to the population standard deviation divided by the square root of n. This is
called the central limit theorem. And it not only holds true for these simple
populations but for any population. Because of the central limit theorem, we can
have a population of any shape. And then let's say we draw a sample from it and
calculate the mean, and then we draw another sample from it and calculate the
mean. And we keep doing this, say a 100 times. Assuming the sample size is large
enough, if we plot the distribution of means, we're going to get something
that's relatively normal. With a standard deviation equal to the population
standard deviation divided by the square root of the sample size. And we've been
calling it SE so far. And that's because this is called the standard error. This
is super cool, but I also understand that it's also super complicated. So we're
going to go through a few more ways of looking at this, using applets and
demonstrations. And then finally at the end of this lesson, go over an example
where we would actually use this in real life.