Why Not Go MAD? Exercise 41 shows that the sample variance s2 is an unbiased estimator of s2. Do the following with the same population of {3, 6, 9} to show that the mean absolute deviation of a sample is a biased estimator of the mean absolute deviation of a population.

a. Find the mean absolute deviation of the population {3, 6, 9}.

b. List the nine different possible samples of two values selected with replacement, then find the mean absolute deviation for each of them. If you repeatedly select two sample values, what is the mean value of the mean absolute deviations?

c. Based on the results of parts

(a) and (b), does the mean absolute deviation of a sample tend to target the mean absolute deviation of the population? Does division by n 2 1 instead of division by n make the mean absolute deviation an unbiased estimate of the mean absolute deviation for the population?