A study examined how long aircraft air-conditioning units operated after being r

Question

A study examined how long aircraft air-conditioning units operated after being repaired. Here are the operating times (in hours) for one unit:
97 51 11 4 141 18 142 68 77 80 1 16 106 206 82 54 31 216 46 111 39 63 18 191 18 163 24

(a) Make a histogram of these data, using 40-hour classes, starting with 0 = time < 40, 40 = time < 80, . . . .

(b) Describe the overall shape of the distribution. Is it roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers?

(c) Is the five-number summary or the mean and standard deviation a better brief summary for this distribution?
Explain your choice. Calculate the one of these summaries that you choose.

Explanation / Answer

1a.it takes a lot of time to draw a histogram but you have to make the intervals 0-39.99 1, 4 , 11, 16,18, 18, 18, 24, 31, 39 total 10 40-79.99 46, 51, 54 , 63, 68, 77 total 6 80-119.99 80 ,106, 82, 111 total 4 120-159.99 141, 142 total 2 160-199.99 163, 191 total 2 200-239.99 206, 216 total 2 you can draw it now the width must be 40, and on the vertical axes put the total. 1b. skewed right, no outliers (obviously no low outliers; max = 216 < 1.5*(111-18)+111 = 250.5, so no high outliers) 1c. 5-number summary is better because of the skew: min=1, Q1=18, median=54, Q3=111, max=216

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