A data set is formed by recording the sums of 100 rolls of a pair of dice. A second data set is formed by again rolling a pair of dice 100 times but recording the product, not the sum, of the two numbers.

(A) Which of the two data sets would you expect to have the smaller standard deviation? Explain.

(B) To obtain evidence for your answer to part (A), use a graphing calculator to simulate both experiments, and compute the standard deviations of each of the two data sets.