Concept explainers
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 to what happened to the mean over the four-year period? How? What happened to the shapes of the underlying distribution?
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 |
3.13
a. Compute the median and mean scores for these data.
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 |
b. These same 25 students completed the same survey during the senior year. Compute the median and mean for this second set of scores, and compare them to the earlier set. What happened?
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 |
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