Question

What is the third quartile of the set of data shown below 26, 34, 38, 49, 65, 75, 81

Answer 1

Population size:7

Lower quartile (xL): 34

Median (xm): 49

Upper quartile (xU): 75

Answer 2

The third quartile is
`Q_3=75`

Explanation:

Given : Data 26, 34, 38, 49, 65, 75, 81

To find : What is the third quartile of the set of data?

Solution :

First arrange the data from smallest to greatest.

26, 34, 38, 49, 65, 75, 81

Then find the median of the data,

Since, the data is in odd numbers median is mid term i.e. 49.

To find the third quartile we take the upper half of data

Upper half of data set, 65, 75, 81

Third quartile is the median of the upper half of the data.

Median of upper half is

`Q_3=((n+1)^(th))/(2)`

`Q_3=((3+1)^(th))/(2)`

`Q_3=2^(th)` term

`Q_3=75`

Therefore, The third quartile is
`Q_3=75`