Question

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed.

41  54  61  48  27  27  41  54  61  31  48  41  47
​(a) Find the sample mean and sample standard deviation.
​(b) Each employee in the sample is given a 5​% raise. Find the sample mean and sample standard deviation for the revised data set.
​(c) To calculate the monthly​ salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set.
​(d) What can you conclude from the results of​ (a), (b), and​ (c)?

Answer 1

Down

Explanation:

List from low to high

27 27 31 41 41 41 47 48 48 54 54 61 61

a. Mean = sum of sample/2

Mean = 581 / 2 = 290.5

b. Mean + 5%

290.5 + 5% = 305.025

c. 305.025 / 12 = 25.41875

d. Mean is ratio. Thus the adding and dividing with anything will affect the mean overall