Question

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?

Answer 1

Answer:

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.