# 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?

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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Step 1
Let M, L, N be the mean, median, mode of the old data set.
Here, the number of employees is $=\left(25000/2500\right)=10$.
Let the salaries of 10 employees be ${S}_{i}$, where $i=1,2,3,4,5,6,7,8,9,10$.
Then, $M=\frac{\sum _{i=1}^{10}{S}_{i}}{10}$
L is the number in the middle when the data is ordered from least to greatest.
$L={S}_{j}$, where $j\in \left(1,2,3,4,5,6,7,8,9,10\right)$.
$N={S}_{k}$, where $j\in \left(1,2,3,4,5,6,7,8,9,10\right)$, 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 $=\frac{\sum _{i=1}^{10}\left({s}_{i}+2500\right)}{10}=\frac{\sum _{i=1}^{10}{S}_{j}}{10}=M+2500$
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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