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). You should be able to copy these and paste them into Excel. 40 40 45 50 50 50 55 60 75 90 (a) Determine the range, population variance, and population standard deviation for the data. (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) $2,500. Add the bonuses under this plan to the original salaries to create a new data set. Recalculate the range, population variance, and population standard deviation. How do they compare to the originals? Asked another way, what happens to the mean, the standard deviation, and the variance when you add a constant to each value in the data set? Why? (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 range, population variance, and population standard deviation. How do they compare to the originals? Asked another way, what happens to the mean, the standard deviation, and the variance when you multiply a constant to each value in the data set? Why? (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 range, population variance, and population standard deviation. How do they compare to the originals? Why?

Answer 1