Q 86. - The Practice of Statistics for AP

Question

Mean salary? Last year a small accounting firm paid each of its five clerks $\backslash (22,000$, two junior accountants $\backslash )50,000$ 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.

Step-by-Step Solution

Answer

The mean and median salary is $\$60, 000$ and $\$25, 000$respectively

There are seven employees who earn less than the mean salary $(\$60,000)$

Step 1: Given information

Five clerks - $\$22,000$

Two junior accountants - $\$50,000$ each,

The firm’s owner - $\$270,000$

Step 2: Concept

The mean of a data set is determined by adding all of the numbers in the set and dividing by the number of values in the set. The median is the value in the middle of a data set when it is arranged from smallest to largest. The mode is the number that appears the most frequently in a data set.

Step 3: Calculation

The mean compensation would be $\$22, 000$ for five clerks, $\$50, 000$ for two junior accountants, and $\$270,000$ for the firm's owner.

Mean: $$\begin{gathered} \overline{X} =\frac{sum of observations}{n} \\ = \frac{x_1+ x_2+ x_3+.....+ x_n}{n} \\ \overline{X}= \frac{\Sigma Xi}{N} \\ \Sigma X = \frac{22000+22000+22000+22000+50000+50000+270000}{8} \\ = \frac{480000}{8} \\ \overline{X}=\$60, 000 \end{gathered}$$

Seven employees make less than the average income.

The data shows that seven employees earn less than the median pay $(\$60,000)$, including five clerks, two junior accountants, and the firm's owner, who earns $\$270,000$. The mid-value $(\$22, 000; \$22, 000; \$22, 000; \$22, 000; \$22, 000; \$50,000; \$50, 000; \$270,000)$ is the median for the supplied data. There is no centre of observation because the number of data values is even. In the data, there is a centre pair, $\$22, 000 and \$22, 000,$ with three observations preceding them and three observations following them in the order list. The average of these two observations is the median. 

Median: $$\begin{gathered} M = \frac{ N+1}{2}th observation \\ =\frac{ 8+1}{2} \\ = 4.5 th Observation \\ = \frac{4 th observation+5 th observation}{2} \\ = \frac{25000+25000}{2} \\ M = \$25, 000 \end{gathered}$$

An unethical recruiter could use this information to deceive a potential employee. Because the mean is substantially greater than the median, which is influenced by the firm owner's compensation. The salary of the form owner is an extreme value, skewing the distribution to the right.

As a result, the average and median salaries are $\$60, 000$ and $\$25, 000,$ respectively, with seven employees earning less than the average $(\$60,000)$