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:

Maximum Load (short-tons)	Number of Cables
9.3-9.7	22
9.8-10.2	55
10.3-10.7	12
10.8-11.2	17
11.3-11.7	14
11.8-12.2	66
12.3-12.7	33
12.8-13.2	11

Solution:

Maximum Load (short-tons)	Number of Cables (f)	Class Bounderies	Cumulative Frequencies
9.3-9.7	2	9.25-9.75	2
9.8-10.2	5	9.75-10.25	2 + 5 = 7
10.3-10.7	12	10.25-10.75	7 + 12 = 19
10.8-11.2	17	10.75-11.25	19 + 17 = 36
11.3-11.7	14	11.25-11.75	36 + 14 = 50
11.8-12.2	6	11.75-12.25	50 + 6 = 56
12.3-12.7	3	12.25-12.75	56 + 3 = 59
12.8-13.2	1	12.75-13.25	59 + 1 = 60

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