The interquartile range

Quartiles are the summary measures that divide a ranked data set into four equal parts. Three measures will divide any data set into four equal parts. These three measures are the first quartile (denoted by ), the second quartile (denoted by ), and the third quartile (denoted by ). The data should be ranked in increasing order before the quartiles are determined. The quartiles are defined as follows:

- ordered observation

- ordered observation.

The difference between the third and the first quartiles gives the interquartile range. That is

.

Example:

A teacher gives a 20-point test to 10 students. The scores are shown below

18, 15, 12, 6, 8, 2, 3, 5, 20, 10

Find the interquartile range.

Solution:

First, we rank the given data in increasing order:

2, 3, 5, 6, 8, 10, 12, 15, 18, 20

- ordered observation.

.

Hence, the first quartile is three-quarter way from the data (3) to the third (5). Therefore,

First quartile=

Similarly, since

The third quartile is one-quarter of the way from the observation (15) to the observation (18). Thus we have

Third quartile= .

Finally, the interquartile range is the difference between the third and first quartiles:

Interquartile range=

Example:

The following are the ages of nine employees of an insurance company

47, 28, 39, 51, 33, 37, 59, 24, 33

Find the interquartile range.

Solution:

Let us arrange the data in order from smallest to largest

24, 28, 33, 33, 37, 39, 47, 51, 59

The interquartile range is

.

Дата добавления: 2015-08-05