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?

phepafalowl 2022-07-26 Answered
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 mean for the new data set is nothing, thousand dollars.
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Answers (1)

Mira Spears
Answered 2022-07-27 Author has 14 answers
Step 1
Let M, L, N be the mean, median, mode of the old data set.
Here, the number of employees is = ( 25000 / 2500 ) = 10.
Let the salaries of 10 employees be S i , where i = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10.
Then, M = i = 1 10 S i 10
L is the number in the middle when the data is ordered from least to greatest.
L = S j , where j ( 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ).
N = S k , where j ( 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ), which occurs most in the given data.
Step 2
Now, the salaries of 10 employees with bonus is S j + 2500, where j = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10.
For the new data set,
Mean = i = 1 10 ( s i + 2500 ) 10 = i = 1 10 S j 10 = M + 2500
Median = S j + 2500 = L + 2500.
Mode = S k + 2500 = N + 2500.
Therefore, for the new data set, both of mean, median, mode increases to $2500.
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