Quartile deviation for Grouped 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 grouped data. 

 

For Grouped Data

  

Problem: Following are the observations showing the age of 50 employees working in a whole sale center. Find the quartile deviation and coefficient of quartile deviation. 

 

 

 

Solution: 

In case of frequency distribution, quartiles can be calculated by using the formula: 

 

 

 

 

 

First Quartile (Q1)

  

In case of frequency distribution first quartile can be calculated by using the formula given below: 

 

 

 

Third Quartile (Q3)

  

Like first and second quartile, the third quartile can be calculated by using the formula: 

 

 

 

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

 

 

 

See also calculation of quartile deviation for ungrouped data