Statistics - Quartile Deviation

Statistics – Quartile Deviation

It depends upon the decrease quartile Q1Q1 and the higher quartile Q3Q3. The distinction Q3Q1Q3−Q1 is named the inter quartile vary. The distinction Q3Q1Q3−Q1 divided by 2 is named semi-inter quartile vary or the quartile deviation.

System

Q.D.=Q3Q12Q.D.=Q3−Q12

Coefficient of Quartile Deviation

A relative measure of dispersion primarily based on the quartile deviation is named the coefficient of quartile deviation. It’s characterised as

Coefficient of Quartile Deviation =Q3Q1Q3+Q1Coefficient of Quartile Deviation =Q3−Q1Q3+Q1

Instance

Downside Assertion:

Calculate the quartile deviation and coefficient of quartile deviation from the info given beneath:

Most Load
(short-tons)
Variety 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

Answer:

Most Load
(short-tons)
Variety 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

Worth of n4thn4th merchandise =Worth of 604th604th factor = 15th15th merchandise. Thus Q1Q1 lies in school 10.25-10.75.

Q1=1+hf(n4c)Where l=10.25, h=0.5, f=12, n4=15 and c=7,=10.25+0.512(157),=10.25+0.33,=10.58Q1=1+hf(n4−c)The place 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

Worth of 3n4th3n4th merchandise =Worth of 3×604th3×604th factor = 45th45th merchandise. Thus Q3Q3 lies in school 11.25-11.75.

Q3=1+hf(3n4c)Where l=11.25, h=0.5, f=14, 3n4=45 and c=36,=11.25+0.514(4536),=11.25+0.32,=11.57Q3=1+hf(3n4−c)The place 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.=Q3Q12=11.5710.582,=0.992,=0.495Q.D.=Q3−Q12=11.57−10.582,=0.992,=0.495

Coefficient of Quartile Deviation

Coefficient of Quartile Deviation =Q3Q1Q3+Q1=11.5710.5811.57+10.58,=0.9922.15,=0.045