The Editor’s Report in the November 2003 issue of Technometrics provides the following information regarding the length of time taken to review articles that were submitted for publication during the year 2002. A few articles took longer than 9 months to review, these are omitted from the table.

Question

a. Construct a histogram for these data.

b. Which class interval contains the median review time?

c. Which class interval contains the first quartile of the review times?

d. Which class interval contains the third quartile of the review times?

Answer 1

(a)



(b) The sample size is 171, so the median is the value in position (171 + 1)?2 = 86 when the values are arranged in order. There are 45 + 17 + 18 = 80 values less than or equal to 3, and 80 + 19 = 99 values less than or equal to 4. Therefore the class interval 3 – < 4 contains the median.

(c) The sample size is 171, so the first quartile is the value in position 0.25(171 + 1) = 43 when the values are arranged in order. There are 45 values in the first class interval 0 – < 1. Therefore the class interval 0 – < 1 contains the first quartile.

(d) The sample size is 171, so the third quartile is the value in position 0.75(171 + 1) = 129 when the values are arranged in order. There are 45 + 17 + 18 + 19 + 12 + 14 = 125 values less than or equal to 6, and 125 + 13 = 138 values less than or equal to 7. Therefore the class interval 6 – < 7 contains the third quartile.