Introduction

In the previous chapter of the NCERT Class 11 Statistics for Economics course you studied how to sum up a whole set of data into a single representative value — a measure of central tendency such as the mean, median or mode. Useful as it is, such an average tells only one thing about a distribution: a typical, central size. It says nothing about how much the individual values are scattered around that centre. This chapter studies the measures that quantify exactly that scatter — the variability, or dispersion, of the data.

A short conversation makes the point. Three friends — Ram, Rahim and Maria — are chatting over tea and start comparing their family incomes. Ram says his family of four has an average income of ₹15,000 per member. Rahim says the average in his family of six is also ₹15,000. Maria says her family of five (one of whom is not working) has an average income of ₹15,000 too. They are surprised, because they know Maria's father earns a very large salary. When they look at the actual figures, the puzzle is solved:

Although the average is identical, the individual incomes differ a great deal. In Ram's family the differences are comparatively small; in Rahim's they are larger; and in Maria's they are the largest of all. Knowing only the average is clearly insufficient — a second value that reflects the quantum of variation improves our understanding of the distribution considerably. Per-capita income, for example, gives only the average; a measure of dispersion can reveal the income inequalities behind it, and so tell us about the relative standards of living of different sections of society.

Dispersion is the extent to which the values in a distribution differ from the average of that distribution.

To quantify this variation there are four numerical measures, plus one graphic method:

1. Range
2. Quartile Deviation
3. Mean Deviation
4. Standard Deviation

and, apart from these, a graphic method — the Lorenz Curve — for estimating dispersion. Range and quartile deviation measure dispersion by the spread within which the values lie, while mean deviation and standard deviation measure the extent to which the values differ from the average.

Studying this chapter should enable you to know the limitations of averages, appreciate the need for measures of dispersion, enumerate the various measures of dispersion, calculate them and compare them, and distinguish between absolute and relative measures of dispersion. These NCERT Class 11 Statistics for Economics notes on measures of dispersion, with fully worked examples and previous-year style questions and answers, are meant to build that understanding step by step.