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.
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 Si, where i = 1,2,3,4,5,6,7,8,9,10.
Then, M =
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, where j (1,2,3,4,5,6,7,8,9,10), which occurs most in the given data.
Now, the salaries of 10 employees with bonus is Sj+2500, where j = 1,2,3,4,5,6,7,8,9,10.
For the new data set,
Mean = = = M+2500
Median = Sj+2500 = L+2500.
Mode = Sk+2500 = N+2500.
Therefore, for the new data set, both of mean, median, mode increases to $2500.
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