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16 October, 05:46

The table shows data for a class's mid-term and final exams Which data set has the largest IQR?

Mid-Term Final

100 98

100 95

100 93

95 91

95 88

92 82

92 78

88 78

85 65

75 60

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  1. 16 October, 07:32
    0
    Putting the numbers in order;

    Mid-term numbers: 100 100 100 95 95 92 92 88 85 75

    Median = (95 + 92) / 2 = 93.5

    First quarter = Q1 = 100 100 100 95

    Median of first quarter = (100 + 100) / 2 = 100

    Third quarter = Q3 = 92 88 85 75

    Median of third quarter = (88 + 85) / 2 = 86.5

    Interquartile range (IQR) can be calculated by subtracting Q3 from Q1;

    IQR of mid-term = 86.5 - 100 = - 13.5

    Now putting the final term numbers in order;

    Final-term numbers: 98 95 93 91 88 82 78 78 65 60

    Median = (88 + 82) / 2 = 85

    First quarter = Q1 = 98 95 91 88

    Median of first quarter = (95 + 91) / 2 = 93

    Third quarter = Q3 = 78 78 65 60

    Median of third quarter = (78 + 65) / 2 = 71.5

    Interquartile range (IQR) can be calculated by subtracting Q3 from Q1;

    IQR of final-term = 71.5 - 93 = - 21.5

    Thus the IQR of mid-term is the largest.
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