Question

Find the median, first quartile, third quartile, and interquartile range of the data.

Answer 1

Given:

The data set is:

68, 74, 67, 72, 63, 70, 78, 64, 76

To find:

The median, first quartile, third quartile, and interquartile range of the data.

Solution:

We have,

68, 74, 67, 72, 63, 70, 78, 64, 76

Arrange the given data in ascending order.

63, 64, 67, 68, 70, 72, 74, 76, 78

Now divide the data in two equal parts.

(63, 64, 67, 68), 70, (72, 74, 76, 78)

So, the median of the given data set is 70.

Divide each parenthesis in two equal parts.

(63, 64), (67, 68), 70, (72, 74), (76, 78)

Now, the first quartile is:

$Q_1=\dfrac{64+67}{2}$

$Q_1=\dfrac{131}{2}$

$Q_1=65.5$

The third quartile is:

$Q_3=\dfrac{74+76}{2}$

$Q_3=\dfrac{150}{2}$

$Q_3=75$

The interquartile range (IQR) is the difference between third quartile and first quartile.

$IQR=75-65.5$

$IQR=9.5$

Therefore, median is 70, first quartile is 65.5, third quartile is 75 and the interquartile range is 9.5.