The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 1-46414-253-X
ISBN 13: 978-1-46414-253-6

Chapter 2 - Describing Distributions with Numbers - Apply Your Knowledge - Page 57: 2.8

Answer

Yes, the long travel time of 60 minutes is a suspected outlier.

Work Step by Step

The IQR rule states that an observation is a suspected outlier if that observation falls more than 1.5 IQRs above the third quartile or below the first quartile. $(5, 10, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 60)$ The median of the set is 20. The $Q_{1}$ value of the set is 10 (the average of the 4th and 5th data points, both of which are 10). The $Q_{3}$ value of the set is 30 (the average of the 4th and 5th data points, both of which are 30). $IQR = Q_{3}-Q_{1}$ $IQR = 30 - 20 $ $IQR = 10$ Suspected outliers are 1.5 * IQR above the third quartile or below the first quartile. Suspected outliers are 1.5 * 10, or 15, above the third quartile or below the first quartile. Thus, outliers are 15 + $Q_{3}$ (and higher) and 15 - $Q_{1}$ (and lower). $15 + Q_{3}$ $15 + 30 = 45$ $15 - Q_{1}$ $15 - 20 = -5$ Thus, outliers are greater than 45 and less than -5. The only value that is in the data set that is a suspected outlier is 60.
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