a. Compute the standard deviation for both sets of data presented in problem 3.13 and reproduced here. Compare the standard deviation computed for freshmen with the standard deviation computed for seniors. What happened? Why? Does this change relate at all to what happened to the mean over the fouryear period? How? What happened to the shapes of the underlying distributions?

Freshmen 10 43 30 30 45 40 12 40 42 35 45 25 10 33 50 42 32 38 11 47 22 26 37 38 10 Seniors 10 45 35 27 50 35 10 50 40 30 40 10 10 37 10 40 15 30 20 43 23 25 30 40 10

b. Frequency distributions for both freshman and seniors are presented here. Use this information to compute a mean and standard deviation for each group, and compare these values with the actual mean and standard deviation you computed earlier. How accurate are the SW approximate mean and standard deviation as compared to the actual statistics?

Freshman Scores Frequency (f)

10–19 5 20–29 3 30–39 8 40– 49 8 50–59 01 N
25 Seniors Scores Frequency (f)

10–19 7 20–29 4 30–39 6 40– 49 6 50–59 02 N
25