Page 137 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 7.2 Objectives of Measuring Dispersion

The main objectives of measuring dispersion of a distribution are:
1. To test reliability of an average: A measure of dispersion can be used to test the reliability
of an average. A low value of dispersion implies that there is greater degree of homogeneity
among various items and, consequently, their average can be taken as more reliable or
representative of the distribution.
2. To compare the extent of variability in two or more distributions: The extent of variability
in two or more distributions can be compared by computing their respective dispersions.
A distribution having lower value of dispersion is said to be more uniform or consistent.
3. To facilitate the computations of other statistical measures: Measures of dispersions are
used in computations of various important statistical measures like correlation, regression,
test statistics, confidence intervals, control limits, etc.
4. To serve as the basis for control of variations: The main objective of computing a measure
of dispersion is to know whether the given observations are uniform or not. This knowledge
may be utilised in many ways. In the words of Spurr and Bonini, “In matters of health,
variations in body temperature, pulse beat and blood pressure are basic guides to diagnosis.
Prescribed treatment is designed to control their variations. In industrial production,
efficient operation requires control of quality variations, the causes of which are sought
through inspection and quality control programs”. The extent of inequalities of income
and wealth in any society may help in the selection of an appropriate policy to control
their variations.

Self Assessment

State whether the following statements are true or false:
6. A measure of dispersion can be used to test the reliability of an average.
7. A high value of dispersion implies that there is greater degree of homogeneity among
various items.
8. The extent of variability in two or more distributions can be compared by computing
their respective dispersions.

9. A distribution having lower value of dispersion is said to be more uniform or consistent.
10. Measures of dispersions are used in computations of various important statistical measures
like correlation, regression, test statistics, confidence intervals, control limits, etc.

7.3 Characteristics of a Good Measure of Dispersion

Like the characteristics of a measure of central tendency, a good measure of dispersion should
posses the following characteristics:
1. It should be easy to calculate.

2. It should be easy to understand.
3. It should be rigidly defined.
4. It should be based on all the observations.
5. It should be capable of further mathematical treatment.

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