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?

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.