Q.A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.

A central value tells you where a distribution is centred, but not how spread out it is — and two distributions with the same average can be very different.

A measure of central tendency (mean, median or mode) sums up a whole distribution in a single representative value, but it reveals nothing about the variability of the data. Two distributions can share the same average yet be quite different in spread — recall the three families in the chapter's opening, each with an average income of ₹15,000 but with very different individual incomes.

A measure of dispersion fills this gap by quantifying how far the values lie from the average. It lets us:

1. judge the reliability of the average — a small dispersion means the average is representative, a large one means it is not;
2. compare the consistency of two or more distributions (for example the reliability of two batsmen or two brands); and
3. reveal inequalities that an average hides — such as income inequality behind a per-capita figure.

For these reasons a measure of dispersion is a valuable supplement to the central value: the average locates the distribution, while the dispersion describes the scatter around it, and only the two together give a full understanding of a frequency distribution.