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Fifteen commute times, in minutes, have this five-number summary: minimum 5, first quartile 25, median 40, third quartile 65, maximum 150. Which value, if any, is a potential outlier?
A150 minutes, since it exceeds 125
B5 minutes, since it falls below 25
CNo value lies outside the fences
D150 minutes, since it exceeds 105
Answer & Solution
Correct answer: A. 150 minutes, since it exceeds 125
1. Compute the interquartile range: IQR = 65 - 25 = 40 minutes.
2. Multiply by 1.5: 1.5 x 40 = 60 minutes.
3. The upper fence is the third quartile plus that amount: 65 + 60 = 125 minutes.
4. The lower fence is the first quartile minus it: 25 - 60 = -35 minutes.
5. The maximum, 150 minutes, exceeds the 125-minute fence, so it is flagged as a potential outlier.
6. The minimum, 5 minutes, is above -35, so the low end is clean.
7. Option B misreads the first quartile as a fence; quartiles alone never flag outliers.
8. Option D computes the fence with 1.0 IQR instead of 1.5, giving 105 and the right value for the wrong reason.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.2 Measures of the Location of the Data_
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