Chapter 7, Problem AP2.1CPT

To determine

To find: the maximum possible length of the right-side “whisker”.

Answer to Problem AP2.1CPT

33

Explanation of Solution

Given:

  $\min .=5,Q_1=18,median=20,Q_3=40,\max .=75$

Formula used:

  $IQR=Q_3-Q_1$

For outliers

  $\left[Q_1-1.5IQR,Q_3+1.5IQR\right]$

Calculation:

  $\begin{array}{c}IQR=Q_3-Q_1\\ =40-18\\ =22\end{array}$

  $\begin{array}{c}\left[Q_1-1.5IQR,Q_3+1.5IQR\right]\\ =\left[18-1.5\left(22\right),40+1.5\left(22\right)\right]\\ =\left[18-33,40+33\right]\\ =\left[-15,73\right]\end{array}$

Box plot, the whisker lengths can only be a maximum of 33.

Anything outside of the range would be considered an outlier.

Hence, the correct option is (a)