Given:
The data values are:
21, 32, 17, 24, 15, 30, 28 and 26.
To find:
The first quartile, third quartile, and interquartile range.
Solution:
We have,
21, 32, 17, 24, 15, 30, 28, 26
Arrange the data values in ascending order.
15, 17, 21, 24, 26, 28, 30, 32
Divide the data set in two equal parts.
(15, 17, 21, 24), (26, 28, 30, 32)
Divide each parenthesis in two equal parts.
(15, 17), (21, 24), (26, 28), (30, 32)
Now, the first quartile is:
[tex]Q_1=\dfrac{17+21}{2}[/tex]
[tex]Q_1=\dfrac{38}{2}[/tex]
[tex]Q_1=19[/tex]
The third quartile is:
[tex]Q_3=\dfrac{28+30}{2}[/tex]
[tex]Q_3=\dfrac{58}{2}[/tex]
[tex]Q_3=29[/tex]
The interquartile range is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=29-19[/tex]
[tex]IQR=10[/tex]
Therefore, the first quartile is 19, third quartile is 29 and the interquartile range is 10.
