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.

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? The mean for the new data set is nothing, thousand dollars.

Mira Spears · Accepted Answer

Step 1Let 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 2Now, 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  +  2500Median   =      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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