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Linear Transformations Benjamin owns a small Internet
Chapter 3, Problem 39E(choose chapter or problem)
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
(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?
Questions & Answers
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
(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:Step 1 of 4
Given Benjamin’s salaries (in thousands of dollars) are
30, 30, 45, 50, 50, 50, 55, 55, 60, 75.
a). We have to determine the mean, median, and mode for salary.
Thus, the mean is
\(\begin{aligned} \mu & =\frac{\sum x}{n} \\ & =\frac{30+30+45+50+50+50+55+55+60+75}{10} \\ & =\frac{500}{10} \\ & =50 \\ & =50,000 \$ \text { (in thousands) } \end{aligned}\)
The median is the average of the 5th and 6th values.
That is,
\(\begin{aligned} \text { Median } & =\frac{50+50}{2} \\ & =50 \\ & =50,000 \$ \text { (in thousands) } \end{aligned}\)
The mode is the most repeated value in the data set.
That is,
\(\begin{aligned} \text { Mode } & =50 \\ & =50,000 \$ \text { (in thousands) } \end{aligned}\)
Therefore, mean = 50,000$, median = 50,000$, mode = 50,000$.