# Statistics – Quartile Deviation

It depends on the lower quartile Q1Q1 and the upper quartile Q3Q3. The difference Q3−Q1Q3−Q1 is called the inter quartile range. The difference Q3−Q1Q3−Q1 divided by 2 is called semi-inter quartile range or the quartile deviation.

## Formula

Q.D.=Q3−Q12Q.D.=Q3−Q12

## Coefficient of Quartile Deviation

A relative measure of dispersion based on the quartile deviation is known as the coefficient of quartile deviation. It is characterized as

Coefficient of Quartile Deviation =Q3−Q1Q3+Q1Coefficient of Quartile Deviation =Q3−Q1Q3+Q1

### Example

Problem Statement:

Calculate the quartile deviation and coefficient of quartile deviation from the data given below:

Solution:

### Q1Q1

Value of n4thn4th item =Value of 604th604th thing = 15th15th item. Thus Q1Q1 lies in class 10.25-10.75.

Q1=1+hf(n4−c)Where l=10.25, h=0.5, f=12, n4=15 and c=7,=10.25+0.512(15−7),=10.25+0.33,=10.58Q1=1+hf(n4−c)Where l=10.25, h=0.5, f=12, n4=15 and c=7,=10.25+0.512(15−7),=10.25+0.33,=10.58

### Q3Q3

Value of 3n4th3n4th item =Value of 3×604th3×604th thing = 45th45th item. Thus Q3Q3 lies in class 11.25-11.75.

Q3=1+hf(3n4−c)Where l=11.25, h=0.5, f=14, 3n4=45 and c=36,=11.25+0.514(45−36),=11.25+0.32,=11.57Q3=1+hf(3n4−c)Where l=11.25, h=0.5, f=14, 3n4=45 and c=36,=11.25+0.514(45−36),=11.25+0.32,=11.57

### Quartile Deviation

Q.D.=Q3−Q12=11.57−10.582,=0.992,=0.495Q.D.=Q3−Q12=11.57−10.582,=0.992,=0.495

### Coefficient of Quartile Deviation

Coefficient of Quartile Deviation =Q3−Q1Q3+Q1=11.57−10.5811.57+10.58,=0.9922.15,=0.045