Chapter 1.3, Problem 94E

(a)

To determine

To calculate the meanand median of the given data.

Answer to Problem 94E

Mean = $70000

Median = $32000

Explanation of Solution

Given:

5 Clerks = $32000

2 junior accountants = $60000

Firm’s owner = $280000

Calculation:

  $\begin{array}{c}\text{Mean = }\frac{5\times 32000+2\times 60000+1\times 280000}{5+2+1}\\ =70000\end{array}$

The number of employees who earn less than mean salary = 5 + 2 = 7.

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{\left(\frac{8}{2}\right)}^{\text{Th term}}+{\left(\frac{8}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{4^{\text{Th term}}+5^{\text{Th term}}}{2}\\ =\frac{32000+32000}{2}\\ =32000\end{array}$

(b)

To determine

To explain the way these statistics can be used as misleading data.

Explanation of Solution

The mean salary of the given firm is very high and if the company shows that mean salary of the employees is 70,000 then it will be a misleading figure. Since the salary of employees also includes the outlier values like the salary of Owner which is considerable very high as compared to the rest of the employees.

In this situation, the company should prefer to use the median salary as median does not affected by the outliers.