Question

The first quartile of a data set is 32, and the third quartile is 52. One of these values in the data set is an outlier. Which of the following is this?

A. 23
B. 3
C. 63
D. 83

Answer 1

Answer: D. 83

Step-by-step explanation:

Given: The first quartile of a data set is
`Q_1=32`, and the third quartile is
`Q_2=52`.

The formula of to calculate the interquartile range is :-

`IQR= Q_3 - Q_1= 52-32= 20`

The lower limit of interval for the data having no outlier :-

`Q_1-1.5(IQR)=32-1.5(20) = 2`

The upper limit of interval for the data having no outlier:-

`Q_3+1.5(IQR)=52+1.5(20) = 82`

Since 83 is the value which lies outside the interval or greater than the upper limit.

Therefore, outlier for the data = 83.

Answer 2

As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier

so...the 83 is outlier
so correct option is D
hope it helps