Index Number and Indexes

Introduction

Index numbers are a statistician's way of expressing the difference between two measurements by designating one number as the "base", giving it the value 100 and then expressing the second number as a percentage of the first.

or

A measure of the value of a variable relative to its value at some base date or state (the base period). The index is often scaled so that its base value is 100. Such an index may be described as a base-weighted index

Mathematical representation of Index

Index number is basically a ratio of two quantity.For volume q and price p and the value V of the transactions in any commodity,

Q = V / P

Other formulas of index number are as follow and few of them are explained later

Let be the price per unit in period , be the quantity produced in period , and be the value of the units. Let be the estimated relative importance of a product. There are several types of indices defined, among them those listed in the following table.

index abbr. formula

Bowley index

Fisher index

geometric mean index

harmonic mean index

Laspeyres' index

marshall-Edgeworth index

mitchell index

Paasche's index

Walsh index

Examples

If the population of a town increased from 20,000 in 1988 to 21,000 in 1991, the population in 1991 was 105% of the population in 1988. Therefore, on a 1988 = 100 base, the population index for the town was 105 in 1991.

An "index", as the term is generally used when referring to statistics, is a series of index numbers expressing a series of numbers as percentages of a single number.

Uses Of Index Number

Indexes can be used to express comparisons between places, industries, etc. but the most common use is to express changes over a period of time, in which case the index is also a time series or "series". One point in time is designated the base period—it may be a year, month, or any other period—and given the value 100. The index numbers for the measurement (price, quantity, value, etc.) at all other points in time indicate the percentage change from the base period.

If the price, quantity or value has increased by 15% since the base period, the index is 115; if it has fallen 5%, the index is 95. It is important to note that indexes reflect percentage differences relative to the base year and not absolute levels. If the price index for one item is 110 and for another is 105, it means the price of the first has increased twice as much as the price of the second. It does not mean that the first item is more expensive than the second.

Each index number in a series reflects the percentage change from the base period. It is important not to confuse an index point change and a percentage change between two index numbers in a series.

Example: if the price index for butter was 130 one year and 143 the next year, the index point change would be:

143 – 130 = 13