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