Question

A statistics student gave a survey to students which asked how many first cousins they have. The data from the first nine responses are shown below.
6, 2, 7, 8, 8, 8, 5, 10, 10

What is the IQR of the data?

2.52 first cousins
3 first cousins
3.5 first cousins
8 first cousins

Answer 1

Given:

Date set for number of cousins is

6, 2, 7, 8, 8, 8, 5, 10, 10

To find:

The IQR of the data.

Solution:

We have,

6, 2, 7, 8, 8, 8, 5, 10, 10

Arrange the data ascending order.

2, 5, 6, 7, 8, 8, 8, 10, 10

Divide the data in two equal parts.

(2, 5, 6, 7), 8,( 8, 8, 10, 10)

Divide each parenthesis in two equal parts.

(2, 5), (6, 7), 8, (8, 8), (10, 10)

Now,

$Q_1=\dfrac{5+6}{2}$

$Q_1=\dfrac{11}{2}$

$Q_1=5.5$

and,

$Q_3=\dfrac{8+10}{2}$

$Q_3=\dfrac{18}{2}$

$Q_3=9$

The interquartile range (IQR) of the  data set is

$IQR=Q_3-Q_1$

$IQR=9-5.5$

$IQR=3.5$

The IQR is 3.5 first cousins.

Therefore, the correct option is C.