Measures of Dispersion
it includes:
- Range (R)
- Inter-quartile Range
- Quartile Deviation
- Standard Deviation
What is Range?
It is the difference between the highest and lowest value of the series.
It is denoted by (R)
R= H-L where
H is the highest value
L is the lowest value
Coefficient of R =H-L/H+L
How to determine:
A) Individual series:
find R and Coefficient of R
3,8,2,5,6,9,10
Sol: -
R = H-L
H=10
L=2
put into formula
R = 10-2 =8
Coefficient of R =H-L/H+L
= 10-2/10+2
=8/12
= 0.67
This was an individual series, Next.
B) Discrete Series: -
There is a same formula, but the highest value and the lowest value are in X series(variable) not in Y series(variable).
R= H-L
H: highest value of X
L: Lowest value of X
 |
| Do not see frequency of Y |
H =50
K=10
put values in the formula
R= 50-10 = 40
Coefficient of R = H-L/H+L
= 50-10/50+10
= 40/60
= 0.67
C) Continuous Series
there are two ways in this series
Class interval method
Mixed value method
1. Class interval method
H=60 which is highest value
L=10 which is lowest value
R= 60-10
= 50
Coefficient of R = H-L / H+L
= 60-10 / 60+10
=50/70
=0.714
2. Mid value method
 |
| mid value is central value of C.T |
R=H-L
H: 55 is the highest value
L: 15 is the highest value
R= 55-15
=40
Coefficient of R = H-L /H+L
=55-15/55+15
=40/70
=0.57
That was our Range.
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