Chapter 1.3, Problem 86E

To determine

To find: the mean and median salary paid and the number of the employees who earn less than the mean

Answer to Problem 86E

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

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

Explanation of Solution

Given:

Five clerks - $22,000

Two junior accountants - $50,000 each,

The firm’s owner - S270.000

Calculation:

If the firm has paid $22, 000 to five clerks, $50, 000 to two junior accountants and $270,000 to the firm's owner then the mean salary would be

Mean:

  $\begin{array}{c}\overline{X}=\frac{\text{sum}\text{of}\text{observations}}{n}\\ =\frac{x_1+x_2+x_3+\mathrm{...}+x_n}{n}\\ \overline{X}=\frac{{\displaystyle \sum X_i}}{N}\\ {\displaystyle \sum X}=\frac{22000+22000+22000+22000+50000+50000+270000}{8}\\ =\frac{480000}{8}\\ \overline{X}=\$60,000\end{array}$

There are seven employees who earn less than mean salary.

The median for the data is:

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

i.e. $22, 000 to five clerks, $50, 000 to two junior accountants and $270,000 to the firm's owner.

The median for the given data is the mid value ($22, 000; $22, 000; $22, 000; $22, 000; $22, 000; $50, 000; $50, 000; $270,000). Since there is an even number of data values, there is no centre of observation. There is a centre pair i.e. $22, 000 and $22, 000 in the data which have 3 observations before them and 3 observations after them in the order list. The median is the average of these two observations.

Median:

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

Here the data can be used by unethical recruiter to mislead the prospective employee. Because mean is much higher than median which is affected by the salary paid to the firm owner. Form owner's salary is an extreme value which has made the distribution skewed towards right.

Conclusion:

Therefore, the mean and median salary is $\$60,000$ and $\$25,000$ respectively and there are seven employees who earn less than mean salary ($60,000)