Unformatted text preview: ute measure of dispersion gives the variation in
rainfall in mm. On the other hand relative measures of
dispersion are free from the units of measurements of the
observations. They are pure numbers. They are used to
compare the variation in two or more sets, which are having
different units of measurements of observations.
The various absolute and relative measures of
dispersion are listed below.
Absolute measure
Relative measure
1. Range
1.Coefficient of Range
2.Quartile deviation 2.Coefficient of Quartile deviation
3.Mean deviation
3. Coefficient of Mean deviation
4.Standard deviation 4.Coefficient of variation
7.3 Range and coefficient of Range:
7.3.1 Range:
This is the simplest possible measure of dispersion and
is defined as the difference between the largest and smallest
values of the variable.
In symbols, Range = L – S.
Where
L = Largest value.
S = Smallest value.
142 In individual observations and discrete series, L and S
are easily identified. In continuous series, the following two
methods are followed.
Method 1:
L = Upper boundary of the highest class
S = Lower boundary of the lowest class.
Method 2:
L = Mid value of the highest class.
S = Mid value of the lowest class.
7.3.2 Coefficient of Range :
L −S
Coefficient of Range =
L+S
Example1:
Find the value of range and its coefficient for the following
data.
7, 9, 6, 8, 11, 10, 4
Solution:
L=11, S = 4.
Range
= L – S = 11 4 = 7
L −S
Coefficient of Range =
L+S
11 − 4
=
11 + 4
7
= 0.4667
=
15
Example 2:
Calculate range and its co efficient from the following
distribution.
Size:
6063 6366 6669 6972 7275
Number:
5
18
42
27
8
Solution:
L = Upper boundary of the highest class.
= 75
143 S = Lower boundary of the lowest class.
= 60
Range = L – S = 75 – 60 = 15
L −S
Coefficient of Range =
L+S
75 − 60
=
75 + 60
15
=
= 0.1111
135
7.3.3 Merits and Demerits of Range :
Merits:
1. It is simple to understand.
2. It is easy to calculate.
3. In certain types of problems like quality control, weather
forecasts, share price analysis, et c., range is most...
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 Winter '08
 Moshiri
 Business, Statistics

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