Measures of Dispersion, Meaning, Definition, Objectives, Properties,Absolute and Relative Measures,Methods of Measuring Dispersion

                     Measures of Dispersion

 Introduction

The various measures of central tendency or averages discussed in the previous chapter give us only one single figure that represents the entire set of data. But the average alone cannot describe the set of observations fully. It does not reveal the degree of spread out or extent of variability may be the same but still there can be wide disparities in the formation of the series. In such a case, necessary to study the variability or dispersion of the observations. Measures of dispersion help us to study the variability of the items, i.e., the extent to which the items vary from one another and from it becomes the central value.

 

Meaning of Dispersion

The term dispersion is generally used in two senses: Firstly, dispersion refers to the variations of the items among themselves. If the value of all the items of a series is the same, there will be no variation among the various items and the dispersion will be zero. On the other hand, the greater the variation among different items of a series, the more will be the dispersion. Secondly, dispersion refers to the variation of the items around an average. If the difference between the value of items and the average is large, the dispersion will be high and on the other hand, if the difference between the value of the items and the average is small, the dispersion will be low. Thus, dispersion is defined as scattered or spreads of the individual items in a given series.

 

Definition of Dispersion

Some important definitions of dispersion are given below:

1.  According to Bowley “Dispersion is a measure of the variations of the items.”

2. According to Connor “Dispersion is a measure of the extent to which the individual items vary.”

Objectives of Measuring Dispersion

The measures of dispersion are helpful in statistical investigation. Some of the main objectives of dispersion are as under:

(1) To determine the reliability of an average: The measures of dispersion help in determining the reliability of an average. It points out how far an average is representative of a statistical series. If the dispersion or variation is small, the average will closely represent the individual values and it is highly representative. On the other hand, if the dispersion or variation is large, the average will be quite unreliable.

(2) To compare the variability of two or more series: The measures of dispersion helps in comparing the variability of two or more series. It is also useful to determine the uniformity or consistency of two or more series. A high degree of variation would mean less consistency or less uniformity as compared to the data having less variation.

(3) For facilitating the use of other statistical measures: Measures of dispersion serves the basis of many other statistical measures such as correlation, regression, testing of hypothesis, etc. These measures are based on measures of variation of one kind or another.

(4) Basis of Statistical Quality Control: The measures of dispersion is the basis of statistical quality control. The extent of the dispersion gives an indication to the management as to whether the variation in the quality of the product is due to random factors or if there is some defect in the manufacturing process. On the basis of this analysis, the management may take suitable measures to control the cause of variation in the quality of the product.

Properties of a Good Measure of Dispersion

A good measure of dispersion should possess the following properties:

(1) It should be easy to understand.

(2) It should be simple to calculate.

(3) It should be uniquely defined.

(4) It should be based on all observations.

(5) It should not be unduly affected by extreme items.

(6) It should be capable of further algebraic treatment.

Absolute and Relative Measures of Dispersion

Absolute Measure of Dispersion: Absolute measure of dispersion is expressed in the same unit in which data of the series are expressed. They are expressed in the same statistical unit, e.g., rupees, kilogram, tons, years, centimeters, etc.

Relative Measure of Dispersion: Relative measure of dispersion refers to the variability stated in the form of ratio or percentage. Thus, the relative measure of dispersion is independent of the unit of measurement. It is also called the coefficient of dispersion. These measures are used to compare two series expressed in different units.

Methods of Measuring Dispersion

The following methods of measuring dispersion:

Positional Measures of Dispersion

(1) Range

(2) Interquartile Range

(3) Quartile Deviation

Mathematical Measures of Dispersion

(4) Mean Deviation

(5) Standard of Deviation

(6) Coefficient oExam Studies