Question

Mean salary? Last year a small accounting firm paid each of its five clerks \(32,000, two junior accountants \)60,000 each, and the firm’s owner $280,000.

(a) What is the mean salary paid at this firm? How many of the employees earn less than the mean? What is the median salary?

(b) Write a sentence to describe how an unethical recruiter could use statistics to mislead prospective employees.

Short answer

Part (a) Mean is $70,000 and Median is $32,000

All employees earn less than the mean salary.

Part (b) By using mean.

Step-by-step solution

Part (a) Step 1. Given information.

The given data is:

32000, 32000, 32000, 32000, 32000, 60000, 60000, 280000

$n=8$

Part (a) Step 2. Find the mean salary paid at this firm.

Mean is:

$$\begin{gathered} \overline{x}=\frac{\sum _{i=1}^n{x}_i}{n} \\ =\frac{32000+32000+32000+32000+32000+60000+60000+280000}{8} \\ =\frac{560000}{8} \\ =70000 \end{gathered}$$

All employees of the firm earn less than the mean salary of $70,000 except the owner.

Part (a) Step 3. Find the median salary.

32000, 32000, 32000, 32000, 32000, 60000, 60000, 280000

As we know that median is the middle value of a data set. As the given set is even, the median will be the average of two middle values (4th and 5th) of this sorted data:

$$\begin{gathered} M=\frac{32000+32000}{2} \\ =32000 \end{gathered}$$

The median salary is $32,000.

Part (b) Explanation.

As we have observed that all employees in the organization make less than the mean, an unethical recruiter might use the mean to deceive prospective recruits, and so the prospective employees will have no possibility of making that much money with this company.