Question

1. 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.

Explanation:

Part (a)

Step 1: Calculate the total salary

First, we find the total salary paid to each group of employees.

• For the five clerks: Each earns $32,000, so total for clerks is \(5\times32000 = 160000\)
• For the two junior accountants: Each earns $60,000, so total for junior accountants is \(2\times60000 = 120000\)
• For the owner: Earns $280,000, so total for owner is \(280000\)

Now, sum these up to get the total salary: \(160000 + 120000 + 280000 = 560000\)

Step 2: Calculate the number of employees

Number of clerks: 5, junior accountants: 2, owner: 1. So total number of employees \(n=5 + 2+ 1=8\)

Step 3: Calculate the mean salary

Mean salary \(\bar{x}=\frac{\text{Total Salary}}{\text{Number of Employees}}=\frac{560000}{8} = 70000\)

Step 4: Determine how many earn less than the mean

• Clerks earn $32,000 which is less than $70,000: 5 employees
• Junior accountants earn $60,000 which is less than $70,000: 2 employees
• Owner earns $280,000 which is more than $70,000: 0 employees

Total employees earning less than mean: \(5 + 2=7\)

Step 5: Calculate the median salary

To find the median, we first order the salaries. The salaries are (in dollars): 32000, 32000, 32000, 32000, 32000, 60000, 60000, 280000.

Since there are 8 (even number) employees, the median is the average of the 4th and 5th values.

The 4th value is 32000 and the 5th value is 32000. So median \(=\frac{32000 + 32000}{2}=32000\)

Part (b)

An unethical recruiter could say something like: "The mean salary at our firm is $70,000, which is a great earning potential for new employees." This misleads because the high salary of the owner (an outlier) inflates the mean, and most employees (the clerks and junior accountants) earn much less than $70,000. The recruiter is using the mean (which is affected by the outlier) instead of a more representative measure like the median to give a false impression of typical earnings.

Answer:

s

(a)

• Mean salary: \(\$70,000\)
• Number of employees earning less than mean: \(7\)
• Median salary: \(\$32,000\)

(b)

An unethical recruiter could state "The mean salary at our firm is $70,000, indicating high earning potential," ignoring that the owner's high salary inflates the mean and most employees earn far less (e.g., clerks at $32,000, junior accountants at $60,000), using the mean to mislead about typical earnings.