Summary Statistics for a Quantitative Variable

AP Statistics· difficulty 4/5

A summary of a data set is given.

Five-Number Summary Min: 15 Q1: 22 Median: 28 Q3: 38 Max: 75

Is the maximum value (75) an outlier by the 1.5×IQR rule?

  • A

    Yes, because 75 > 62 (upper fence)

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  • B

    Cannot determine without raw data

  • C

    No, because 75 < 76

  • D

    No, max values are never outliers

Explanation

IQR = 38 − 22 = 16. Upper fence = 38 + 24 = 62. Since 75 > 62, the value 75 is an outlier.

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