2. Calculate the range, variance, and standard deviation in EXCEL for the SAMPLE below. Then, calculate the range, variance and standard deviation in EXCEL as if the group of numbers was a POPULATION. What numbers changed? What numbers didn't. Explain why each number did or did not change.

4, 1, 5, 7, 5, 19, 6, 9, 5, 6, 5, 5, 5, 4, 5, 2

3. Both variance and standard deviation measure variation in a set of numbers. Why do we need two measures that appear to be doing the same thing? Why isn't one measure sufficient? Discuss how variance and standard deviation measure variation by specifically discussing their formulas. Come to a conclusion about why we there are two measures.Incorporate their formulas into the discussion.

This hint may help you think of why: John, Peter, and Zeus are brothers. Zeus is two inches different in height than Peter. John is also two inches different in height than Peter. However, Zeus and John are not the same height. How is this possible?

Second hint: a negative number multiplied by a negative number is a positive number.

4. The Empirical Rule for a normally distributed population and Chebyshev's Theoremhavethe same basic purpose. In your own words, explain that purpose.

5. Explain the following in your own words: percentile, the first quartile, the third quartile, and the IQR (interquartile range). Use the list of numbers in #2 to find these values.

6. In #2, use the data for the SAMPLE. Assume it is normally distributed, even if it is not. Use the empirical rule to calculate the range of values that are 1 standard deviation from the mean. Show your work. Do the same for two and three standard deviations from the mean.