Chapter 14.2, Problem 24E

To determine

To find: The value of $x$ so that the median of data is $8$ .

Answer to Problem 24E

The value of $x$ is $8$ .

Explanation of Solution

Given:

The set of data is as:

  $\left\{11,2,3,3.2,13,14,8,x\right\}$

Calculation:

Arrange the data in ascending order.

  $\left\{2,3,3.2,8,x,11,13,14\right\}$ .

The median is calculated as:

  $\begin{array}{c}\text{Median}=\frac{1}{2}\left(\left(\frac{N}{2}\right)\text{th term}+\left(\frac{N}{2}+1\right)\text{th term}\right)\\ 8=\frac{4\text{th term}+5\text{th term}}{2}\left[\because \text{Median}=8\right]\\ 8=\frac{8+x}{2}\\ x=8\end{array}$

The value of $x$ is $8$ .