A sample of 20 endangered species was obtained and the length of time (in months) since being placed on the list was recorded for each species. The ordered data follow:
52, 54, 58, 59, 59, 60, 60, 63, 65, 66, 67, 68, 69, 73, 74, 77, 78, 79, 79, 98
Which value would need to be exceeded for a data point to be considered an outlier when using the 1.5 × IQR rule?

Question

Quizplus · Accepted Answer

First, we need to find the IQR:
Q1 = 60 (the median of the first 10 values)
Q3 = 78 (the median of the last 10 values)
IQR = Q3 - Q1 = 18

Then, we can use the 1.5 × IQR rule:
Lower outlier bound: Q1 - 1.5 × IQR = 60 - 1.5 × 18 = 31
Upper outlier bound: Q3 + 1.5 × IQR = 78 + 1.5 × 18 = 105

Since the largest data point is 98, we know that none of the data points are above the upper outlier bound. Therefore, the value that would need to be exceeded for a data point to be considered an outlier is the upper outlier bound, which is 105.

The only answer choice that is greater than 105 is D, so the answer is D.

A Sample of 20 Endangered Species Was Obtained and the Length