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18 September, 16:56

Add three data values to the following data set so the mean increases by 10 and the median does not change. {42, 37, 32, 29, 20}

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  1. 18 September, 20:04
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    Sum of the numbers in the set: 42+37+32+29+20 = 160

    Current mean: 160/5 = 32

    Median = the valvue of the middle = 32.

    New mean: 32+10 = 42.

    Sum of numbers in the new set = 42*8 = 336

    Difference: 336 - 160 = 176

    I want to include 32, so that the new median stays in 32.

    So the other two numbers must add 176 - 32 = 144

    I will use a smaller number than 32 and the other greater (again in order to keep the same median.

    I will choose 28 and 144 - 28 = 116.

    So my three new numbers are 28, 32 and 116 and the new set is {116, 42, 37, 32, 32, 29,28, 20}

    Checking:

    Sum of the terms: 116+42+37+32+32+29+28+20 = 336

    Mean = 336 / 8 = 42, which is 10 more than the original mean.

    And the new median is (32+32) / 2 = 32. The same of the original set.
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