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30 October, 10:35

Here is the five-number summary for a group of 100 runners in a 5-kilometer race. the variable is the time to complete the race. five-number summary: minimum: 15 minutes q1: 27 minutes median: 31 minutes q3: 32 minutes maximum: 50 minutes are there any outliers in the runners' finish times by the 1.5 * iqr definition?

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  1. 30 October, 10:55
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    Given:

    Minimum = 15 min

    Q1 = 27 min, the 25 quartile

    Q2 = 31 min, the median

    Q3 = 32 min, the 75% quartile

    Maximum = 50 min

    Calculate the IQR (Inter quartile range).

    IQR = Q3 - Q1 = 32 - 27 = 5

    To detect outliers, use the k = 1.5 test.

    The expected range is

    [Q1 - 1.5*IQR, Q3 + 1.5*IQR]

    = [27 - 1.5*5, 32 + 1.5*5]

    = [19.5, 39.5]

    The actual range is [15, 50].

    The minimum is less than 19.5.

    The maximum is greater than 39.5

    Therefore outliers exist.

    Answer: There are outliers.
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