## ← M&M CLT - Intro to Descriptive Statistics

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Showing Revision 3 created 05/25/2016 by Udacity Robot.

1. Good job. So the mean should be the same as the population mean. And the
2. standard error should be the population standard deviation divided by the square
3. root of the sample size. Which is about 1.56. So remember, since these are the
4. theoretical mean and standard error based on all possible samples of size five
5. from this population, they probably won't get exactly the same standard error as
6. what we found. But they should come pretty close. >> So let's see what they got.
7. The standard error of the mean computed using this formula, derived from the
8. central limit theorem is sigma 3.49 and divided by the square root of our sample
9. size 5. So that's 3.49 Divided by the square root of 5 or n, that comes out to
10. be roughly 1.56. If we took the true standard error of the mean, in other words,
11. computed the actual standard deviation for all of the sample means we just took,
12. that value is 1.57. Very, very close to that given by the formula. In checking
13. the distribution of sample means The sampling distribution of the mean here was
14. approximately normal; not perfectly normal, but pretty close. So all in all, we
15. see the central limit theorem works. It provides us a useful tool that we'll use
16. for the rest of the semester. So, hurray for the central limit theorem!