Question

Benjamin owns a small Internet business. Besides himself, he employs nine other people. The salaries earned by the employees are given next in thousands of dollars (Benjamin's salary is the largest, of course): 30, 30, 45, 50, 50, 50, 55, 55, 60, 75.
Required:
a. Determine the mean, median, and mode for salary.
b. 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) $2500. 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?
c. As a second option. Benjamin can give each employee a bonus of 5% of his or her original salary. Add the bonuses under this second plan to the original salaries to create a new data set. Recalculate the mean, median, and mode. How do they compare to the originals?
d. As a third option, Benjamin decides not to give his employees a bonus at all. Instead, he keeps the $25,000 for himself. Use this plan to create a new data set. Recalculate the mean, median, and mode. How do they compare to the originals?

Answer 1

Answer:

a) mean μ = 50     median M = 50   mode Md = 50

b) mean μ₂ = 52,5 median M = 52,5   mode Md = 52,5 all vales increased in 2,5 ( thousands of $) the same quantity of individuals incements

c) mean  μ₃ = 52,50 median M = 52,5 mode Md = 52,5 The same values obtain in b)

d) mean  μ₃ = 52,50 median M = 50 and Mode 50

Step-by-step explanation:

a) Mean μ is the average then:

30 30 45 50 50 50 55 55 60 75

μ = 50

The median M, is the central (fifth value) 50

And the mode

Md = 50

b) Adding 2,5 ( in thousands of $) to each one of the employees

32,5 32,5 47,5 52,5 52,5 52,5 57,5 57,5 62,5 77,5

The mean    μ₂ = 52,5 $, since the average value has to be increased by the common increased number

The median M = 52,5   and also the mode Md = 52,5

c)  31,5 31,5 47,25 52,5 52,5 52,5 57,75 57,75 63 78,75

The mean  μ₃ = 52,50

The median M = 52,50

The Mode Md = 52,50

d) 30 30 45 50 50 50 55 55 60 100

μ₄ = 52,5

Median M = 50

Mode Md = 50