Introduction to Index Numbers

An index number is a special kind of average that measures the relative change in some economic quantity — most commonly price, but also quantity, or value — between one time period (called the base period) and another (called the current period). Unlike an ordinary average, which summarises data recorded in the same units at a single point in time, an index number summarises change over time and expresses that change as a single percentage figure, with the base period always fixed at 100.

Two time periods are compared. The base year (or base period), denoted by the subscript 0, is the year chosen as the point of reference — its own index value is always taken as 100, however many rupees its prices actually were. The current year (or given year), denoted by the subscript 1, is the year whose prices are being compared against the base year. The symbol $p_0$ denotes the price of a commodity in the base year, and $p_1$ denotes the price of the SAME commodity in the current year. A price index number for the current year, written $P_{01}$, then tells us, as a single percentage, how much prices in general have risen or fallen relative to the base year.

Business and government use price index numbers constantly — to track inflation (the general price index), to revise wages and pensions in line with the cost of living, to compare the real purchasing power of money across years, and to deflate figures like national income so that genuine growth can be separated from a mere rise in prices. Three standard methods of constructing a price index number are studied in this chapter — the Simple Aggregate Method, the Weighted Aggregate Method, and the Cost of Living Index (also called the Family Budget Method) — each combining the price data of several commodities into one representative figure, but each doing so differently.

This chapter is part of the WBCHSE Class 12 Business Mathematics and Basic Statistics syllabus's Statistics unit; the technique of building a price index from a base year — Simple Aggregate, Weighted Aggregate, and the Cost of Living Index — is the same core statistical method used to compute official price and cost-of-living indices, so the reasoning learnt here carries well beyond the West Bengal syllabus alone.