Chapter 14.2, Problem 31E

(a)

To determine

To find: The mean of the salaries.

Answer to Problem 31E

The mean of the salaries is $87800$ .

Explanation of Solution

Given:

The given data of salaries of ten employee are as:

  $\begin{array}{l}\$54000,\$75000,\$55000,\$62000,\$226000,\$65000,\\ \$59000,\$61000,\$162000,\$59000\end{array}$

Calculation:

The mean is calculated as:

  $\begin{array}{c}\text{Mean}=\frac{\left[\begin{array}{l}54000+75000+55000+62000+226000+65000\\ +59000+61000+162000+59000\end{array}\right]}{10}\\ =87800\end{array}$

The mean of the salaries is $87800$ .

(b)

To determine

To find: The median of the salaries.

Answer to Problem 31E

The median of the salaries is $61500$ .

Explanation of Solution

After arranging the data in ascending order, the median is calculated as: $\begin{array}{c}\text{Median}=\frac{n}{2}\text{th term}+\left(\frac{n}{2}+1\right)\text{th term}\\ \text{=}\frac{\left(\text{10th term}+\text{11th term}\right)}{2}\\ =\frac{61000+62000}{2}\\ =61500\end{array}$

The median of the salaries is $61500$ .

(c)

To determine

To find: The mode of the salaries.

Answer to Problem 31E

The mode of the salariesis $59000$ .

Explanation of Solution

The mode is the most occurring number in the data, so the mode is given as:

  $\text{Mode}=59000$ .

The mode of the salaries is $59000$ .

(d)

To determine

To find: The measure of central tendency might an employee can use when asking for a raise.

Answer to Problem 31E

The employee can use the mean.

Explanation of Solution

The mean considered as the best measure of central tendency so an employee will use the mean. That he can use when asking for a raise.

Therefore an employee can use the mean.

(e)

To determine

To find: The measure of central tendency might management use to argue against a raise for an employee.

Answer to Problem 31E

The measure of central tendency might management use is mode.

Explanation of Solution

Since the mode is the least measure of central tendency so the management can use mode to argue against a raise for an employee.

The measure of central tendency might management use is mode.

(f)

To determine

To find: The measure of central tendency that is most representative of the data.

Answer to Problem 31E

The median is the most representative of the data.

Explanation of Solution

Since the Mean is affected by the extreme values of $162000\text{and}226000$ and only two people make less than mode.

So the median is the most representative of the data.

(g)

To determine

To write: The convincing argument that you deserve a raise in salary when making salary $\$75000$ .

Answer to Problem 31E

The reason is given below.

Explanation of Solution

Here is a convincing argument that you deserve a raise:

I have been with the company for many years, and I am still making less than the mean salary.

The explanation is given above.