Chapter 10.3, Problem 7E

Solution

To calculate: The median of the data of the salaries for employees in a department of a company.

The median of the data of the salaries for employees in a department of a company is $33.5$ .

Given information: The data of the salaries for employees in a department of a company in thousand dollars is:

  $\begin{array}{l}33.5,35.3,33.8,29.3,36.7,32.8,31.7,37.3,33.5,28.2,34.8,\\ 33.5,29.7,38.5,32.7,34.8,34.2,31.6,35.4\end{array}$

Formula used: If the list of $n$ numbers $\left\{x_1,x_2,\dots ,x_n\right\}$ is arranged in ascending or descending order, then median is the middle number if $n$ is odd and median is the average of two middle numbers if $n$ is even.

Calculation:

To find the median of the given data, arrange the list of numbers is ascending order.

  $\begin{array}{l}28.2,29.3,29.7,31.6,31.7,32.7,32.8,33.5,33.5,33.5,\\ 33.8,34.2,34.8,34.8,35.3,35.4,36.7,37.3,38.5\end{array}$

It can be observed that this is the list of $19$ numbers. So, the middle number of the list is the median of the data.

From the list, the middle number obtained is $33.5$ .

Thus, the median of the given data is $33.5$ .