Question

The numbers of members in 8 workout clubs are 100, 95, 90, 85, 85, 95, 100, and 90. Suppose that a new workout club opens and immediately has 160 members. Is the number of members at this new club an outlier? 160 members an outlier.

Answer 1

A data value ( here 160 ) is an outlier if

x < Q1 - 1.5 IQR

x > Q3 + 1.5 IQR

IQR - interquartile range

Data set is: 85,85,90,90,100,100.     Q3 = 97.5,  IQR = 97.5 - 87.5 = 10

160 > Q3 + 1.5 IQR

160 > 97.5 + 1.5 * ( 97.5 - 87.5 )

160 > 97.5 + 1.5 * 10

160 > 97.5 + 15

160 > 112.5    ( correct )

Answer: The number of members at this new club is an outlier.