Consider the data set 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 12.

a. Obtain the mean and median of the data.

b. Replace the 10 in the data set by 100 and again compute the mean and median. Decide which measure of center works better here, and explain your answer.

c. For the data set in part (b), the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result?