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,
[tex]Q_1=\dfrac{5+6}{2}[/tex]
[tex]Q_1=\dfrac{11}{2}[/tex]
[tex]Q_1=5.5[/tex]
and,
[tex]Q_3=\dfrac{8+10}{2}[/tex]
[tex]Q_3=\dfrac{18}{2}[/tex]
[tex]Q_3=9[/tex]
The interquartile range (IQR) of the  data set is
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=9-5.5[/tex]
[tex]IQR=3.5[/tex]
The IQR is 3.5 first cousins.
Therefore, the correct option is C.
