Meaning AND Definition
An index number is a statistical tool used in economics and business to quantify changes in an
individual variable or a group of variables concerning geographical locations, time, or other
aspects.
The primary objective of this statistical measure is to simplify complex comparisons.
An index number is a statistical measure, designed to measure changes in a variable, or a group
of related variables”.
“Index number is a single ratio (or a percentage) which measures the combined change of
several variables between two different times, places or situations”.
If the index number is used to measure the relative change in just one variable, such as hourly
wages in manufacturing, it is referred to as a simple index.
An index number can also be used to measure changes in the value of the group of variables
such as prices of specified list of commodities, volume of production in different sectors of an
industry, production of various agricultural crops, cost of living etc, it is referred to as composite
index.
Index number measures average change in a group of related variables over two different
situations such as prices of specified list of commodities, volume of production in different
sectors of an industry, production of various agricultural crops, cost of living etc.
Index number does not indicate that the change is uniform for all commodities or group of
related variables used to calculate it.
Mathematical usage
Conventionally, index numbers are expressed in terms of percentage.
Of the two periods, the period with which the comparison is to be made, is known as the
base period.
The value in the base period is given the index number 100. Suppose the change in price in
the year 2013 is measured in comparison to the year 2000, then 2000 become the base year
and 2013 becomes the current year.
For Example By saying that the price index for the year 2013 is 125, taking base year as
2000, it means that there is an increase of 25% in the general price as compared to the
corresponding figure for the year 2000.
Price index numbers measure and permit comparison of the prices of certain goods.
Quantity index numbers measure the changes in the physical volume of production,
construction or employment.
Attributes
Index numbers are a special type of average that provides a measurement of relative changes in
the level of a certain phenomenon from time to time. It is a special type of average because it
can be used to compare two or more series which are composed of different types of items or
even expressed in different types of units.
Index numbers are expressed in terms of percentages to show the extent of relative change.
Index numbers measure relative changes. They measure the relative change in the value of a
variable or a group of related variables over a period of time or between places.
Index numbers can also measure changes which are not directly measurable. For Example the
cost of living, the price level or the business activity in a country are not directly measurable but
it is possible to study relative changes in these activities by measuring the changes in the values
of variables/factors which affect these activities.
Application
1. Index numbers are economic barometers. Index numbers measure the level of business and economic
activities and are therefore helpful in gauging the economic status of the country.- Understanding the
ideas of Stock exchanges, SENSEX, Inflation and deflation.
2. Index numbers helps in formulating suitable economic policies and planning.- while deciding the
increase of DA of the employees; the employers have to depend primarily on the cost of living index. If
salaries or wages are not increased according to the cost of living it leads to strikes, lock outs etc.
3. Index numbers are used in studying trends and tendencies.- Understanding community preferences
across different markets and their demand for different commodities and services.
4. Index numbers are useful in forecasting future economic activity.
5. Index numbers measure the purchasing power of money.- Understanding whether the money values
are up or down to ensure that human needs meet the ends.
Price Index and its Mathematical Application
Price index, measure of relative price changes, consisting of a series of numbers arranged so that a
comparison between the values for any two periods or places will show the average change in prices
between periods or the average difference in prices between places. Price indexes were first developed
to measure changes in the cost of living in order to determine the wage increases necessary to maintain
a constant standard of living. Price index numbers measure and permit comparison of the prices of
certain goods. The price indices can be constructed and explained through a mathematical schedule.
Construction of the Price Index Table
The price index of commodities can be calculated using different methods, broadly classified into two-
Weighted and Unweighted, for better understanding.
a. Un-weighted Index - In the un-weighted index number the weights are not assigned to the various
items used for the calculation of index number.
a.1 i) Simple Aggregate Method
This method is based on the assumption that various items and their prices are quoted in same units.
Equal importance is given to all the items. The formula for a simple aggregative price index is given as
follows:
Example 1
a.2 (ii) Simple Average of Price Relatives Method
This method is an improvement over the previous method as it is not affected by the unit in which the
prices of various commodities are quoted. The price relatives are pure
number and therefore are independent of original units in which these are
quoted. The price index number using price relatives is defined as follows:
where P1 and P0 indicate the price of the ith commodity in the current period and base period
respectively. The ratio (P1/P0) × 100 is also referred to as price relative of the commodity and n stands
for the number of commodities.
Example 1 eh with the values given here
b. Weighted Index Number
In weighted index number rational weights are assigned to all the items or commodities. Such weights
indicate the relative importance of the items included in the calculation of the index. In most cases
quantity of usage is the best measure of importance.
