# Measures of Dispersion in Statistics

Dispersion measures the extent to which the different items tend to disperse away from the central tendency. In other words, while central tendency indicates a representative value, the measures of dispersion indicate the divergence of the values of different items from the central value. Thus, measures of dispersion provide a complete and comprehensive picture of the statistical series.

## Importance of the Study of Dispersion.

Reliability of average: Dispersion measures the extent to which the values of different items in the series differ from the central value. By measuring the extent of variability it can be judged how well a central tendency is able to represent the values in the series. A high value of dispersion indicates that the central value does not appropriately represent the values in the series. On the opposite hand, a coffee value of dispersion indicates that the central value is a good representative of the data. Thus, a measure of dispersion helps in judging the reliability of the central value.

Comparison of different series: Measures of dispersion facilitate the comparison of different series with regard to uniformity and homogeneity. A low dispersion indicates high uniformity and vice-versa. Measures of dispersion are used to assess variables such as the profits of a firm, the value of shares, etc. For example, a low dispersion in the data for profits over different years indicates consistency in the profit earnings of the firm over the years.

To control variability: Measures of dispersion helps in identifying the variability in the data. Accordingly, appropriate steps can be taken to control the variability. For example, an identification of the variability in the quality of the production can act as a guide for the firm to take appropriate measures.

Helpful in using other statistical measures: They are not only helpful in measuring the variability in a given data but in fact are useful in other areas also. In other words, it acts as a base in the calculation of higher-order statistical measures such as correlation, regression, etc., and in this way, it becomes important to study dispersion.

## Types of Measures of Dispersion

It can be broadly classified into the following two categories.

• Absolute Measure of Dispersion
• Relative Measure of Dispersion

### Absolute measures of dispersion

It refers to those measures that are expressed in terms of the original unit of series. For example, if the dispersion in the series for income is expressed in rupees then, it refers to the absolute dispersion. Such measures facilitate the comparison of variability in two or more series that are expressed in the same units. Some of the absolute measures of dispersion are range, quartile deviation, mean deviation, and standard deviation.

### Relative measures of dispersion

It refers to those measures that express the variability of data in relative value or percentage. With the help of relative measures comparison of the dispersion can be made for two or more series that are expressed in different units.

For example, in order to compare the variability in the income of workers in India (expressed in rupees) and the variability in the income of the workers in the USA (expressed in dollars), relative, measures of dispersion are used. Some of the relative measures of dispersion are coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, and coefficient of variation.

#### Measures of central tendency

Central tendency refers to a central value that represents the whole statistical series. The central value is sometimes simply referred to as average. The following are the objectives of measures of central tendency.

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