# Introduction

We have already learnt in detail the measures of central tendency - namely mean, median and mode of given data. These measures give a single number as the representative of the whole data. But they do not tell us how the observations are scattered about the average. For example, two distributions giving weekly wages of 200 persons may have the same mean, say, Rs100. In one distribution most of the observations may be cented around the mean value 100; a few others may be away from 100. In an another distribution, a large number of observations may be above 150 and another set of large number of observations may be below 50 and only a few between 50 and 100 and still the mean may be 100.

This fact may be illustrated by a diagram as shown below.
 Wages No. of Workers 25 5 30 7 50 13 75 12 100 15 125 20 150 15 165 7 175 6

 Wages No. of Workers 80 5 90 10 100 50 110 20 120 10
These two distributions with the same mean are not identical. In the first one values are nearer to the mean and in the second one they are spread away from the mean. Similarly, two distributions may have the same median, but the deviations of the observations from the median may be different in the two distributions. In order to study this aspect of distributions, we introduce the concept of dispersion, in this chapter. By dispersion, we mean the Scattering or Spreading of the observations from the central value.

The various measures of dispersion or variability are
1. Range
2. Quartile Deviation
3. Mean Deviation
4. Standard deviation.
The first two are positional measures of dispersion and the last two measures of dispersion are based on all observations.