Page 80 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes find out whether the average calculated is reliable or not. It also helps in comparing the two
series and also help in finding out ways to control the variations. In this way dispersion is a
very strong tool into the hands of statisticians to know about the structure of data more closely
and reliably.
Properties of a Good Measure of Dispersion
Just like the properties of a good measure of central tendency, properties of a good measure of
dispersion are:
W. A. Sppur and C. P. Bonim: Statistical Analysis for Business Decision.
(1) It should be simple to understand.
(2) It must be easy to calculate.
(3) It must be based on all the items of the series.
(4) It should not be unduly affected by the extreme items.
(5) It should be least affected by the fluctuations in sampling.
(6) It should be capable of further statistical treatment.
6.2 Absolute and Relative Measures of Dispersion

Absolute measures of dispersion: When the dispersion of a series is calculated in terms of the absolute
or actual figures in the data and the value of dispersion obtained can be expressed in the same units
as the items of data are expressed, such measures are called absolute measures of dispersion. For
example, if we calculate dispersion of a series indicating the income of group of persons in rupees,
and the value of dispersion is obtained in rupees, it is termed as absolute measure of dispersion.
Relative measures of dispersion: When the value of dispersion is calculated as ratio or percentage of
the average it is called relative measure of dispersion.
6.3 Range, Quartile Deviation and Percentile

Range
‘Range’ is the simplest measure of dispersion which is determined by the two extreme values of the
observations and it is the difference between the largest and the smallest value in a distribution.
Uses of Range: (1) Range is very useful in quality control measures taken by the production
department. It is checked that the quality should not deteriorate beyond the set value of range. Control
charts are prepared for the purpose. (2) Another area where ‘range’ is very useful is the study of
fluctuation of data. Variations in the weather forecasts, movement in the prices of securities etc. can
be studied effectively and efficiently with the help of range.
Merits/advantages: (1) Simple to understand and easy to calculate, (2) It presents a broad picture of
the data.
Demerits/disadvantages: (1) Gets affected by the extreme items, (2) does not take into consideration
towards most of the items and their deviations, (3) Does not give reasonable picture of the data, (4) It
is influenced by fluctuations of sampling.

Formula
Range = Largest Value – Smallest Value
or
Maximum – Minimum
or
Range = L – S
or
M – M
1 0

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