Question

The five-number summary for a data set is given by min = 5, ${\mathrm{Q}}_1=18$, median = 20, ${\mathrm{Q}}_3=40$, max = 75. If you wanted to construct a boxplot for the data set that would show outliers, if any existed, what would be the maximum possible length of the right-side “whisker”?

a. 33

b. 35

c. 45

d. 53

e. 55

Short answer

(a) The maximum possible length of the right-side whisker is 33

Step-by-step solution

Given Information

Consider that $min.=5,{\mathrm{Q}}_1=18,\text{median}=20,{\mathrm{Q}}_3=40,max.=75$

The following concept was used:

$\mathrm{IQR}={\mathrm{Q}}_3-{\mathrm{Q}}_1$

For the scribes.

$\left[{\mathrm{Q}}_1-1.5\mathrm{IQR},{\mathrm{Q}}_3+1.5\mathrm{IQR}\right]$

Explanation for correct option

Consider that,

$\begin{array}{l}\mathrm{IQR}={\mathrm{Q}}_3-{\mathrm{Q}}_1\\ =40-18\\ =22\\ \left[{\mathrm{Q}}_1-1.5\mathrm{IQR},{\mathrm{Q}}_3+1.5\mathrm{IQR}\right]\\ =\left[18-1.5\left(22\right),40+1.5\left(22\right)\right]\\ =\left[-15,73\right]\end{array}$

The whisker lengths on a box plot can only be a maximum of 33

An outlier is anything that falls outside of the range.

Explanation for incorrect option

Option B the maximum possible length of the right-side “whisker” will not be 35

Option C the maximum possible length of the right-side “whisker” will not be 45

Option D the maximum possible length of the right-side “whisker” will not be 53

Option E the maximum possible length of the right-side “whisker” will not be 55