Measures of Dispersion

Meaning

The word dispersion, literally, means deviation, difference, or spread over of certain values from their central value. In relation to a statistical series, it refers to deviation of the various items of a series from their central value, or the difference between any two extreme values of the series.Further, the word ‘measure’ means a method of measuring, or ascertaining certain values. Thus, the phrase ‘measures of dispersion’ means the various possible methods of measuring the dispersions, or deviations of the different values from a designated value of a series. The designated value may be an average value, or any other extreme value. This measure indicates the degree, or the extent to which there are differences between the various items, and the designated value of a series.

Definition

The concept of “measures of dispersion” is so ambiguous that it has been defined variously by the various authors. Some notable definitions are quoted here as under.

• According to A.L .Bowley, “Dispersion is the measure of variation of the items”.
• According to Simpson and Kafka, “The measures of the scatterness of a mass of figures in a series about an average is called measure of variation, or dispersion”.
• According to Spiegel, “The degree to which numerical data lend to spread about an average value is called the variation, or dispersion of the data”.

Essential Characteristics of Dispersion

 “From the foregoing definitions, the essential characteristics of a measure of dispersion can be outlined as under:

• It consists of different methods through which variations can be measured in quantitative manner.
• It deals with a statistical series.
• It indicates the degree, or extent to which the various items of a series deviate from its central value.
• It supplements the measures of central tendency in revealing the characteristics of a frequency distribution.
• It speaks of the reliability, or otherwise of the average value of a series.

Properties of an Ideal Measure of Dispersion

As it will be discussed a little later, there are different types of measures of dispersion each with different types of properties. But a measure of dispersion to be considered as an ideal one should possess the following properties analogous to that of an ideal average:

• It should be rigidly defined and free from any ambiguity.
• It should be simple to follow, and free from any jargon.
• It should be easy for computation, and free from complicated procedure of calculations.
• It should be based on all the items of a series without ignoring any of them.
• It should be capable of further algebraic treatment, and should not violate any algebraic principle.
• It should not be greatly affected by the values of the extreme items of a series.
• It should not be affected by the fluctuation of sampling, and should remain stable in all the cases of samples.