# Quartiles

Sub Topics

In statistics an ordered set of data, three particular items are of special interest. The middle of entire set of items, the middle of the lower half of the items and the middle of the upper half of the items. These are called the quartiles of the data set.

The middle of the lower half of the items is called first quartile or lower quartile, middle of the entire items is called second quartile and the middle of the upper half of the items is called the third quartile or upper quartile.

In a normal distribution, the quartiles give an overall idea about the data set.

### Quartiles Definition:

Quartile is a data which is place exactly one fourth from the set of available information.

## How to Calculate Quartiles

The items of the data are arranged in ascending order.

Obviously the median of the set is the second quartile of the data.

There are two methods by which the lower and upper quartiles are computed.

Method 1

In the ordered set of items, consider the items lower than the median excluding the median. The median of the considered items is the lower quartile of the set.

Similarly consider the items higher than the median excluding the median. The median of the considered items is the upper quartile of the set.

Method 2

This method is same as the previous method excepting that the median is also included in each case.

There is no stipulated rule on choosing the method.

## Examples of Quartiles

Find the quartiles of the set 82, 89, 83. 81, 82, 76, 78, 80, 88, 75, 77

Method 1

The items of the data when arranged in ascending order are,

75, 76, 77, 78, 80, 81, 82, 82, 83, 88, 89

The median of the entire set is 81 and that is the second quartile of the set.

The items lower than the median excluding the median are,

75, 76, 77, 78, 80

The median of this set is 77 and hence it is the lower quartile of the given data set.

The items higher than the median excluding the median are,

82, 82, 83, 88, 89

The median of this set is 83 and hence it is the upper quartile of the given data set.

Method 2

The items of the data when arranged in ascending order are,

75, 76, 77, 78, 80, 81, 82, 82, 83, 88, 89

The median of the entire set is 81 and that is the second quartile of the set.

The items lower than the median including the median are,

75, 76, 77, 78, 80, 81

The median of this set is (77 + 78)/2 = 77.5 and hence it is the lower quartile of the given data set.

The items higher than the median excluding the median are,

81, 82, 82, 83, 88, 89

The median of this set is (82 + 83) = 82.5 and hence it is the upper quartile of the given data set.