Dispersion Measures

The average alone cannot adequately explain a set of observations, unless all the observations are similar. It is necessary to explain the variability or dispersion of the observations. In two or more distributions the central value may be same but still there can be wide disparities in the formation of distribution. The Measurement of dispersion helps us in studying this important characteristic of a distribution.

The dispersion can also be defined as:

The Dispersion is the measure of the variation of the items. The degree to which the numerical data tend to spread about an average value is termed as the variation or dispersion of the data. The Dispersion or spread is the degree of the scatter or variation of the variable about a central value. The measurement of the scatteredness of the mass of figures in a series about an average is known as the measure of variation or disperses. It is clear from above that dispersion is also known as scatter, spread or variation and it  measures the extent to which the items vary from some central value. As the measurement of dispersion gives the average of the differences of various items from an average, they are also known as averages of the second order.

An average is more meaningful when it is examined in the light of dispersion. For e.g., if the average wage of the workers of a factory A is $ 3855 and that of factory B is $ 3990, we cannot necessarily conclude that the workers of factory B are of better wage as in factory B there may be much greater dispersion in the distribution of wages.

Some of its main important topics are as described below:

1. Studying variation-methods

2. Variation significance

3. Mean deviation

4. Mean deviation calculation

5. Arithmetic mean calculation

6. Standard deviation

7. Standard deviation-properties

8. Standard deviation-discrete series

9. Standard deviation-continuous series

10. Variation coefficient

11. Lorenz curve

12. Quartile deviation

13. Tchebycheff's theorem