Question

8. Jamie is a computer network engineer with an annual salary of $61,000, and in her town, there are three consulting firms that each employ four computer programmers, four computer network engineers, and four database administrators. The annual salary information for the employees of each of the consulting firms is shown in the table below.Jamie is employed by consulting firm B, and she wants to know how the mean and median annual salaries of the computer network engineers in her town compare to her own salary, and also how the mean and median annual salaries of the employees at her consulting firm compare to her own salary. (6 points: Part I - 2 points; Part II - 2 points; Part III - 2 points)Part I: What is the mean annual salary of the computer network engineers in Jamie's town? How about the median annual salary of the computer network engineers in Jamie's town?Part II: What is the mean annual salary of the employees at Jamie's consulting firm? How about the median annual salary of the employees at Jamie's consulting firm?Part III: How do the mean and median annual salaries of the computer network engineers in Jamie's town compare to Jamie's salary? How do the mean and median annual salaries of the employees at Jamie's consulting firm compare to Jamie's salary?

Answer 1

Part I: Mean and Median of Computer Network Engineer's in Jamie's town.

`\text{Mean}=(255000+247000+266000)/(12)=(768000)/(12)=64000`

The mean annual salary is $64,000.

Rearranging all the annual salary of the firms (in thousands) we have

57, 66, 63, 69, 61, 59, 65, 62, 70, 64, 60, 72 into

57, 59, 60, 61, 62, 63, 64, 65, 66, 69, 70, 72

Therefore, the median is

`\text{Median}=(62+63)/(2)=63.5`

The median annual salary is $63,500.

Part II: Mean and Median of annual salaries at Jamie's consulting firm (Firm B)

Solving for the mean, we have

`\text{Mean}=(696000)/(12)=58000`

The mean therefore in Jamie's Firm is $58,000.

Rearranging from highest to lowest (in thousands) we have

39, 42, 45, 50, 59, 61, 61, 62, 65, 68, 71, 73

With the two middle values at 61

`\text{Median}=(61+61)/(2)=(122)/(2)=61`

The median in Jamie's firm is $61,000.

Part III: How do the mean and median annual salaries compare to Jamie's

The mean and median for Jamie's town is

Mean = $64,000

Median = $63,500

Compared to Jamie's Salary of $61,000 is much higher than Jamie's

The mean and median for Jamie's consulting firm is

Mean = $58,000

Median = $61,000

Compared to Jamie's salary of $61,000, Jamie's salary is much higher than the mean, while having the same median as Jamie's