Q. 1 - The Practice of Statistics for AP

Question

The five-number summary for a data set is given by $Min=5$, $Q_1=18$, $M=20$, $Q_3=40$, $Max=75$. If you wanted to construct a modified boxplot for the data set (that is, one 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)  (e) $55$

Step-by-Step Solution

Answer

The maximum possible length of the right side is option (a) $33.$

Step 1: Given information

Summary of the data set 

$Min=5$

$Q_1=18$

$M=20$

$Q_3=40$

$Max=75$

To find the maximum length of the right side whisker.

Step 2: Explanation

Initially, we have to find what $I Q R is (IQR=Q3-Q1)$

IQR for this problem is $22(40-18)$

The formula used to find the outliers is to multiply the IQR with $1.5$

Then $22\times 1.5=33$

$33+Q 3 or 33-Q 1$ is the range for values

So this can be the maximum whisker length.

Option (a) 33 is correct.