Chapter 2 - Describing Distributions with Numbers - Apply Your Knowledge: 2.9

40, 40, 40, 43, 45, 57, 50, and 51

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. Per problem 2.7a, the five number summary of the data set is 11, 18, 21, 26, 51. $IQR=Q_{3}−Q_{1}$ $IQR=26−18$ $IQR=8$ Suspected outliers are 1.5 * IQR above the third quartile or below the first quartile. Suspected outliers are 1.5 * 8, or 12, above the third quartile or below the first quartile. Thus, outliers are 12 + $Q_{3}$ (and higher) and $Q_{1}$ - 12 (and lower). $12+Q_{3}$ $12 + 26 = 38$ $Q_{1} - 12$ $18 - 12 = 6$ Thus, outliers are greater than 38 and less than 6. The values that are in the data set and are suspected outliers are 40, 40, 40, 43, 45, 57, 50, and 51.

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