How is the sample mean and sample variance affected if each term in the series is squared?

Question

How is the sample mean and sample variance affected if each term in the series is squared?

Answer 1

You can test this for yourself! If you have a TI-83 calculator (or something similar), click STAT then edit. In L1, type in a handful of values. For example:

1

2

5

6

In L2, type in those values squared:

1

4

25

36

To find the mean and variance, you can click STAT, go over to CALC and choose 1-Var Stats. For the first set of data (when you do 1-Var Stats L1), you'll get a sample mean of 3.5 and a sample standard deviation of 2.380476143. We can turn this into the variance by squaring it, 5.66667.

For the second set of data (when you do 1-Var Stats L2), you'll get different values. Can you try it?