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Unit 6: Dispersion: Meaning and Characteristics, Absolute and Relative Measures of Dispersion including Range...

(the average = 8). In another class, 10 students obtained the following marks. 10, 10, 5, 2, 10, 10, 3, 10, Notes
10 (the average = 8). The dispersion in the second case is more because the size of items in this series
vary considerably, inspite of the fact that the averages of the two have come out to be 8. Some of the
important definitions of dispersion are — As per Brooks and Dick, “Dispersion or spread is the
degree of the scatter or variations of the variable about a central value.” A. L. Bowley defines dispersion
as — “Dispersion is the measure of variations of the item.” In the words of Prof. L. R. Connor,
“Dispersion is a measure of the extent to which the individual items vary.” According to Spriegel,
“The degree to which numerical data tend to spread about an average value is called the variation or
dispersion of data.”
All the above definitions suggest that the term dispersion refers to the variability in the size of items.
This variability is measured with respect to the average of the series. Therefore measures of dispersion
are also termed as averages of the second order.

“A measure of variation or dispersion describes the degree of scatter shown by
observations and is usually measured by comparing the individual values of the
variable with the average of all the values and then calculating the average of all the
individual differences.

Characteristics of Dispersion
There are four basic characteristics of dispersion:
(1) To guage the reliability of the average: Even after making all the efforts to obtain the most
representative average, the efforts prove to be successful when the data is homogeneous. In the
absence of homogeneity, a measure of dispersion presents a better description about the structure
of the distribution and the place of individual items in it. Therefore, in case of heterogeneous
data, dispersion is measured to guage the reliability of the average calculated. When the value
of dispersion is small, it is concluded that the average closely represents the data but when
value of dispersion comes out to be large, it should be concluded that the average obtained is
not very reliable.
(2) To make a comparative study of the variability of series: The consistency of uniformity of two
series can be compared with the help of dispersion. If the value of dispersion measured comes
out to be large, it may be concluded that the series lacks uniformity or consistency. Such studies
are very useful in many fields like profit of companies, share values, performance individuals,
studies related to demand, supply, prices etc.
(3) To identify the factors causing variability so that it can be controlled: Another important
purpose of calculating dispersion is to identify the nature and causes of variations in a given
data so that measures to control these can be suggested. Thus measures of dispersion are not
merely supplementary to the averages, describing their reliability rather, they significantly
disclose the quality of data in terms of homogeneity and consistency. They help to evaluate the
various causes of heterogeneity and inconsistencies and suggest ways to control these. For
example, in industrial production, efficient operation requires control of variation, the causes
of which are sought through, inspection and quality control programmes.” In social sciences,
the measurement of inequality in the distribution of income and wealth requires the measures
of variation.
(4) To serve as a basis for further statistical analysis: Yet another purpose of measures of dispersion
is to help the statistician in carrying out further statistical analysis of the data like studying
correlation, regression, testing of hypothesis, analysis of time series etc.
On the basis of the above, it can be concluded that due to inconsistencies and lack of uniformity
of the data, averages can not prove to be closely representing the data, in most of the cases. In
such a situation, dispersion presents a more better picture about the data, and gives logic to

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