Question 5.57

27. Figure 5.7 (page 193) is a histogram of the tuition and fees charged by the 64 four-year colleges in the state of Massachusetts for the 2014/2015 academic year. Here are those charges (in dollars), arranged in increasing order:

  1. Find the five-number summary and make a boxplot.
  2. What distinctive feature of the Figure 5.7 histogram do these summaries miss? Remember that numerical summaries are not a substitute for looking at the data.
7519 8054 8080 8110 8157 8297 8524 8985
10,355 11,881 12,097 13,258 24,320 26,180 29,012 29,320
29,494 29,930 29,950 30,447 30,859 30,968 31,000 31,000
32,630 32,660 32,830 32,870 33,455 34,060 34,390 35,415
35,532 35,750 36,160 36,215 36,230 37,350 37,426 38,910
40,730 40,954 41,865 42,325 42,511 42,656 43,440 43,498
43,938 44,025 44,222 44,724 45,078 45,080 45,120 45,692
46,664 46,671 47,436 47,710 47,725 48,310 48,488 49,812

27.

(a) , , , , . (If using software, the results for and may differ from the hand calculations above.)

image

(b) The boxplot does not show the two distinctive clusters of values corresponding to the public and private colleges and universities.