This document discusses measures of dispersion, or variation, in data sets. It describes absolute and relative measures of dispersion. Absolute measures give the dispersion in the same units as the original data but cannot be used to compare different data sets. Relative measures are dimensionless and can be used to compare dispersion across data sets. The document then discusses the range as the simplest measure of absolute dispersion. The range is defined as the difference between the maximum and minimum values in a data set. It also defines the coefficient of range, which normalizes the range as a percentage to allow comparison between data sets. Two examples are given to demonstrate calculating the range and coefficient of range.

1. RANGE
NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
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2. Absolute Measure of Dispersion:
Gives an idea about the amount of dispersion/spread in a set of
observations. These quantities measures the dispersion in the
same units as the units of original data. Absolute measures
cannot be used to compare the variation of two or more series/
data set. A measure of absolute dispersion does not in itself, tell
whether the variation is large or small.
Relative Measure of Dispersion:
Relative measures are not expressed in units but it is a pure
number. It is useful for compairing two or more sets of data.

3. Range:
The range is the simplest measure of dispersion; it is the
difference between the maximum and the minimum values in a
data set.
Range = Maximum Value − Minimum Value.
Coefficient of Range 100
Value
Min.
Value
Max.
Value
Min.
Value
Max.





4. Example-1:
The marks obtained by 10 students are given below
36, 45, 32, 50, 41, 39, 49, 32, 46, 38 find
(a) Range (b) Co-efficient of dispersion
Solution:
(a) R = Max.Value – Min.Value
= 50 – 32 = 18 marks
100
.
.
.
.




V
Min
V
Max
V
Min
V
Max
50 32
100 21.95%
50 32

  

(b) Co-efficient of dispersion

5. Example-2:
Find range and coefficient of Dispersion.
C.B F
4 – 8 5
8 – 12 10
12 – 16 15
16 – 20 8
20 – 24 6
Solution:
R = U.C.B of last interval – L.C.B of first interval
R = 24 – 4 = 20
Coefficient of dispersion %
43
.
71
100
4
24
4
24




