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​

Step-by-step 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.