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15 April, 18:29

Business has been good! As a result, Benjamin has a total of $25,000 in bonus pay to distribute to his employees. One option for distributing bonuses is to give each employee (including himself) $2,500. Add the bonuses under this plan to the original salaries to create a new data set. Recalculate the mean, median, and mode. How do they compare to the originals?

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  1. 15 April, 19:44
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    The new data set, which involves the mean, median, mode increases or rise up to $2500.

    Explanation:

    Solution

    Given that:

    Assume that M, L, N be the mean, median, mode of the old data set

    Now

    The number of employees is give as = (25000/2500)

    = 10.

    Suppose the salaries of 10 employees be Si,

    where i = 1,2,3,4,5,6,7,8,9,10.

    Then

    M = ∑^10 i = 1 Si / 10

    Where

    L is the number in the middle when the data is ordered from least to greatest

    L = Sj,

    Where j ∈ (1,2,3,4,5,6,7,8,9,10).

    N = Sk j ∈ (1,2,3,4,5,6,7,8,9,10).

    Thus

    The salaries of 10 employees with bonus is Sj+2500, where j = 1,2,3,4,5,6,7,8,9,10

    Now for the new data set we have the following stated below:

    Mean = ∑^10 i = 1 (Si + 2500) / 10

    = ∑^10 i = 1 Si/10 + 2500

    = M + 2500

    Median = Sj+2500 = L+2500.

    Mode = Sk+2500 = N+2500.

    Hence the new data set, which involves the mean, median, mode increases or rise up to $2500.
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