Question

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 is, one that would show outliers, if any existed), what would be the maximum possible length of the right-side "whisker"? * 2 points 53 35 55 33 45

Answer 1

Answer:

33

Step-by-step explanation:

Values beyond the whiskers of the boxplot are called the outliers :

For a right side Outlier :

Values > Q3 ± 1.5(IQR) ;

IQR = Q3 - Q1)

From the data given:

IQR = (40 - 18) = 22

Hence ; the maximum value of right side whisker will be :

1.5(22) = 33

Answer 2

The maximum possible length of the right-side "whisker" is 33

The given parameters are:

• Min = 15
• Q1 = 18
• Median = 20
• Q3 = 40
• Max = 75

Start by calculating the interquartile range (IQR) using:

$IQR = Q3 -Q1$

So, we have

$IQR = 40 - 18$

$IQR = 22$

The maximum possible length of the right side whisker is then calculated as:

$L = 1.5 \times IQR$

This gives

$L = 1.5 \times 22$

Multiply 1.5 by 22

$L = 33$

Hence, the maximum possible length of the right-side "whisker" is 33

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