Chapter 12.4, Problem 22PPE

To determine

To find: A data set with given parameters.

Answer to Problem 22PPE

Height of the replacement player should be $\le 73.5$ .

Explanation of Solution

Given information:

A data set of $10$ numbers has a median of $22$ , an interquartile range of $10$ , and a minimum of less than $4$ .

Calculation:

A data set of $10$ numbers has a median of $22$ , an interquartile range of $10$ , and a minimum of less than $4$ .

Let us consider a data set as $3,10,15,16,21,23,24,25,32,35.$

  $\begin{array}{l}\text{Minimum }=3<4\\ \text{Median}=\frac{21+23}{2}=22\\ \text{First quartile}\left(Q_1\right)=15\\ \text{Third quartile}\left(Q_3\right)=25\\ \text{Interquartile range}\left(IQR\right)=25-15=10\end{array}$

Hence, a possible data set with given specification can be $3,10,15,16,21,23,24,25,32,35.$