Chapter 7, Problem 1PT2

To determine

The correct answer about the maximum possible length of the right-side “whisker” from the options (a) 33, (b) 35, (c) 45, (d) 53, (e) 55.

Answer to Problem 1PT2

The correct answer is (a).

Explanation of Solution

Given information:

The five-number data set:

  $\text{min}=5$

  $Q_1=18$

  $M=20$

  $Q_3=40$

  $\text{max}=75$

Here, find the IQR from given data.

Write the IQR as:

  $Q_3-Q_1$

Substitute 40 for $Q_3$ and 18 $Q_1$ in $Q_3-Q_1$ .

  $40-18=22$

So, the IQR is 22.

To find the outliers, multiply 1.5 by the IQR that is, 22.

  $22\times 1.5=33$

Since, the range for values allowed in the boxplot is $33+Q_3$ or $33-Q_1$ ; so the “whisker” length can be a max of 33.

Hence, the correct answer is (a).