Chapter 14.3, Problem 21E

To determine

To calculate: Set of numerical data that could be represented by the box-and-whisker plot.

Answer to Problem 21E

  $\left\{15,15,15,16,17,20,24,26,30,35,45,26,\right\}.$

Explanation of Solution

Given information:

  

Formula used:

If each group has the median, the data is divided into four groups. Each group is called quartile.

The difference between the first quartile point and third quartile point is called the inter- quartile range.

The inter- quartile range is divided by 2, the quotient is called the semi- interquartile range.

Median for even terms = $\frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{\left(\frac{n}{2}+1\right)}^{th}\text{term}}{2}$

Median for odd terms = ${\left(\frac{n+1}{2}\right)}^{th}\text{term}$

Calculation:

Consider the box-and-whisker plot

The minimum point is 15 and the maximum point is 45.

The quartile points are

  $\begin{array}{l}{Q}_1=15\\ Q_2=20\\ Q_3=30\end{array}$

The inter- quartile range is $Q_3-Q_1.$

  $\begin{array}{l}=30-15\\ =15\end{array}$

Hence, the set of numerical data is $\left\{15,15,15,16,17,20,24,26,30,35,45,26,\right\}.$