Question

The first quartile of a data set is 72, and the third quartile is 92. Which of these values in the data set is an outlier ?

A. 61
B. 121
C. 101
D. 41​

Answer 1

Answer: Option D

D. 41​

Explanation:

A value
`x_i` is considered an outlier if

`x_i> Q_3 + 1.5IQR`

or

`x_i <Q_1 - 1.5IQR`

Where

`Q_3` is the third quartile

`Q_1` is the first quartile

IQR is the interquartile range.

`IQR = Q_3-Q_1`

In this case:

`Q_3=92\\Q_1=72`

So

`IQR = 92-72 =20`

`Q_3 + 1.5IQR = 92 + 1.5*20 = 122`

`Q_1 - 1.5IQR=72-1.5*20=42`

Then the outlier values will be all those greater than 122 or less than 42

Therefore the answer is the option D.