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Chapter 7: Q. 2.1 (page 488)

The five-number summary for a data set is given by min = 5, Q1=18, median = 20, Q3=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 鈥渨hisker鈥�?

a. 33

b. 35

c. 45

d. 53

e. 55

Short Answer

Expert verified

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

Step by step solution

01

Given Information

Consider that min.=5,Q1=18,median=20,Q3=40,max.=75

The following concept was used:

IQR=Q3鈭�Q1

For the scribes.

Q1鈭�1.5IQR,Q3+1.5IQR

02

Explanation for correct option

Consider that,

IQR=Q3鈭�Q1=40鈭�18=22Q1鈭�1.5IQR,Q3+1.5IQR=18鈭�1.522,40+1.522=鈭�15,73

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

An outlier is anything that falls outside of the range.

03

Explanation for incorrect option

Option B the maximum possible length of the right-side 鈥渨hisker鈥� will not be 35

Option C the maximum possible length of the right-side 鈥渨hisker鈥� will not be 45

Option D the maximum possible length of the right-side 鈥渨hisker鈥� will not be 53

Option E the maximum possible length of the right-side 鈥渨hisker鈥� will not be 55

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