Meaning, Features and Uses of Index Numbers

An index number is a statistical device that measures the average relative change in a group of related variables — such as prices, quantities, or values — over two different periods, one of which is treated as the base period and the other as the current period. The Gujarat board Std 12 Statistics syllabus treats index numbers as one of the most practically useful tools in the whole course, because government agencies, businesses and household budgets all rely on them every single day.

Formally, if $p_0$ denotes the value of a variable in the base year and $p_1$ its value in the current year, a simple index number is expressed as:

The base year is always assigned an index value of 100, and every other year's index is read relative to it. An index of 125 means the variable has risen by 25% over the base year; an index of 90 means it has fallen by 10%.

Features of index numbers

• They are expressed as percentages, but the % sign is conventionally dropped.
• They measure relative change, not absolute change.
• They are averages — usually of a group of relatives, not a single ratio.
• They are specialised averages, since an ordinary average (mean, median) cannot combine items measured in different units (rupees, kilograms, litres) into one figure — index numbers can.

Uses of index numbers (why this chapter carries real weight in the GSHSEB Std-12 Statistics syllabus)

1. Measuring changes in the price level — a rising general price index signals inflation; a falling one signals deflation.
2. Framing economic policy — the RBI and the Government of India use the WPI and CPI to decide monetary policy, dearness allowance, and minimum wages.
3. Deflating — converting money (nominal) values into real values, so wage or income comparisons across years are meaningful (covered fully later in this chapter).
4. Forecasting — trends revealed by index numbers help businesses and planners forecast future demand, cost, and price movements.
5. Comparing — index numbers allow comparison of variables that cannot otherwise be added together (e.g. combining the price change of rice, cloth and fuel into one number).

A useful way to remember it: an index number is "one number that speaks for many."