Quartile Deviation for Ungrouped Data

 Quartile deviation or semi-interquartile range is the dispersion which shows the degree of spread around the middle of a set of data. Since the difference between third and first quartiles is called interquartile range therefore half of interquartile range is called semi-interquartile range also known as quartile deviation. For both grouped and ungrouped data, quartile deviation can be calculated by using the formula:

 

 

Coefficient of Quartile Deviation:

 

Coefficient of Quartile Deviation is used to compare the variation in two data. Since quartile deviation is not affected by the extreme values therefore it is widely used in the data containing extreme values. Coefficient of Quartile Deviation can be calculated by using the formula:

 

 

The concept of quartile deviation and coefficient of quartile deviation can be explained with the help of simple problems for ungrouped data.

 

Ungrouped Data

 

Problem: Following are the runs scored by a batsman in last 20 test matches: 96, 70, 100, 96, 81, 84, 90, 89, 63, 90, 34, 75, 39, 82, 85, 86, 76, 64, 67, and 88. Calculate the Quartile Deviation and Coefficient of Quartile Deviation.

 

Arrange data in ascending order:

 

34, 39, 63, 64, 67, 70, 75, 76, 81, 82, 84, 85, 86, 88, 89, 90, 90, 96, 96, 100

 

First Quartile (Q1)

 

The calculation of First quartile is shown in the figure given below.

 

Third Quartile (Q3)

 

The formula for the calculation of third quartile is given as:

 

By putting the values into the formulas of quartile deviation and coefficient of quartile deviation we get:

 

Also see calculation of Quartile Deviation for grouped data