IntroductionIn the earlier chapter, you have studied how to sum up the data into a single representative value. But that value does not reveal the variability present in the data. In this chapter you will study those measures. Three friends, Ram, Rahim and Maria are chatting over a cup of tea. During the course of their conversation, they start talking about their family incomes. Ram tells them that out of four members in his family, average income per person is Rs 15,000. Rahim says that his family's average income is also same, even though the number of members is six. Maria says that there are five members in her family, out of which one is not working. Average income in her family too, is Rs 15,000. They are a little surprised since they know that Maria's father is earning a huge salary. After they have gathered information, the following data in the form of table arose:
Do you notice that though the average is the same, the number of members in each family is different? It is quite possible that average is nothing but a type of distribution i.e. a representative size of the values. To understand this in the better way, you need to know complete data also. This concept you have seen in Ram's family. (i.e) differences in incomes are comparatively lower. In Rahim's family, differences are higher and in Maria's family are the highest. Knowledge about average is not sufficient. If there is an other value which reflects the quantum of variation in values, your understanding of a distribution improves in the better way.
For example, per capita income gives only the average income. A measure of dispersion can tell you about income inequalities, which improves the understanding of the relative standards of living also enjoyed by different set of society.
Dispersion is the extent to which values in a distribution differ from the average of the distribution.
To quantify the extent of the variation, there are certain measures namely:
- Quartile Deviation
- Mean Deviation
- Standard Deviation