Question

Mean salary? Last year a small accounting firm paid each of its five clerks $22,000, two junior accountants $50,000 each, and the firm's owner $270,000. What is the mean salary paid at this firm? How many of the employees earn less than the mean? What is the median salary? Write a sentence to describe how an unethical recruiter could use statistics to mislead prospective employees.

a) Mean salary: $72,000; Less than mean: 7 employees; Median salary: $50,000; An unethical recruiter could selectively highlight high salaries to mislead prospective employees.
b) Mean salary: $72,000; Less than mean: 5 employees; Median salary: $50,000; An unethical recruiter could manipulate the data to present a falsely low mean salary.
c) Mean salary: $72,000; Less than mean: 2 employees; Median salary: $270,000; An unethical recruiter could exclude certain salaries to inflate the mean.
d) Mean salary: $72,000; Less than mean: 2 employees; Median salary: $50,000; An unethical recruiter could use the median to downplay high salaries.

Answer 1

The mean salary at the accounting firm is $60,000, with 7 out of 8 employees earning less than this amount. The median salary is $50,000. An unethical recruiter might misrepresent these facts to mislead prospective employees.

Step-by-step explanation:

The question asks how to calculate the mean salary, determine how many employees earn less than the mean, find the median salary, and recognize how statistics can be misrepresented.

To calculate the mean salary, we add all the salaries and divide by the total number of employees. Here's the calculation:

• 5 clerks × $22,000 = $110,000
• 2 junior accountants × $50,000 = $100,000
• 1 firm's owner = $270,000
• Total = $110,000 + $100,000 + $270,000 = $480,000
• Mean salary = $480,000 ÷ 8 (Total number of employees) = $60,000

7 employees (5 clerks + 2 junior accountants) earn less than the mean salary. To find the median salary, we list all salaries in ascending order and find the middle value:

1. $22,000 (Clerk)
2. $22,000 (Clerk)
3. $22,000 (Clerk)
4. $22,000 (Clerk)
5. $22,000 (Clerk)
6. $50,000 (Junior Accountant)
7. $50,000 (Junior Accountant)
8. $270,000 (Owner)

The median salary is $50,000, as it is the middle value when the salaries are listed in order. An unethical recruiter could mislead prospective employees by only promoting the top salaries without providing context for salaries at different levels, thus giving a skewed perception of potential earnings.