Question

Use the IQR to determine how many outliers there are in the data set with this

Five Number Summary: 1, 2, 8, 20, 21.

a. 2
b. 3
c. 0
d. 1

Answer 1

Answer: 0 (choice C)

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Step-by-step explanation:

The five number summary is

1. Min
2. Q1
3. Median
4. Q3
5. Max

in that exact order.

A five number summary of 1,2,8,20,21 means:

• Min = 1
• Q1 = 2
• Median = 8
• Q3 = 20
• Max = 21

The IQR (interquartile range) is the distance from Q1 to Q3

IQR = Q3-Q1

IQR = 20-2

IQR = 18

The lower fence (L) is then calculated like so

L = Q1 - 1.5*IQR

L = 2 - 1.5*18

L = -25

If any values are smaller than this lower fence of -25, then they are considered small outliers. But we know that min = 1 is the smallest value. This means we do not have small outliers.

Now onto the upper fence (U)

U = Q3 + 1.5*IQR

U = 20 + 1.5*18

U = 47

If any values are larger than 47, then they are considered large outliers. But we know that max = 21 is the largest value. This means we do not have large outliers.

In summary, all of the data values are between min = 1 and max = 21, which guarantees they are definitely in the interval between L = -25 and U = 47.

This is why there are no outliers in this data set.