Competitive Exams: Index Numbers

how do you define index numbers? Narrate the nature and types of index number with adequate example.

according to Croxton and Cowden index numbers are devices for measuring difference sin the magnitude of a group of related

According to Morris Hamburg in its simplest form an index number is nothing more than a relative which express the relationship between two figures, where one figure is used as a base. According to M L Berenson and D M Levine generally speaking, index number measure the size or magnitude of some object at particular point in time as a percentage of some base or reference object in the past. According to Richard. I. Levin and David S. Rubin an index number is a measure how much a variable changes over time

Nature Of Index Number

  1. Index numbers are specified average used for comparison in situation where two or more series are expressed in different units or represent different items. E. g. Consumer price index representing prices of various items or the index of industrial production representing various commodities produced.

  2. Index number measure the net change in a group of related variable over a period of time.

  3. Index number measure the effect of change over a period of time, across the range of industries, geographical regions or countries.

  4. The consumption of the index number is carefully planned according to the purpose of their computation, collection of data and application of appropriate method, assigning of correct weightages and formula.

Types Of Index Numbers

Price index numbers: A price index is any single number calculated from an array of prices and quantities over a period. Since not all prices and quantities of purchases can be recorded, a representative sample is used instead. Price are generally represented by p in formulae. These are also expressed as price relative, defined as follows

Price relative = (current years price/base years price) * 100, i.e.. = (p1/p0) * 100 any increses in price index amounts to corresponding decreses in purchasing power of the rupees or other affected currency. Quantity index number a quantity index number measures how much the number or quantity of a variable changes over time. Quantities are generally represented as q in formulae. Value index number: a value index number measures changes in total monetary worth, that is, it measure changes in the rupee value of a variable. It combines price and quantity changes to present a more informative index. Composite index number: a single index number may reflect a composite, or group, of changing variable. For instance, the consumer price index measures the general price level for specific goods and service in the economy. These are also known as index numbers. In such cases the price-relative with respect to a selected base are determined separately for each and their statistical average is computed

what are the importance of index numbers used in Indian economy. Explain index numbers of industrial production

Importance Of Index Numbers Used In Indian Economy

Cost of living index or consumer price index

Cost of living index number or consumer price index, expressed as percentage, measure the relative amount of money necessary to derive equal satisfaction during two periods of time, after taking into consideration the fluctuations of the retail prices of consumer goods during these periods. This index is relevant to that real wages of workers are defined as (actual wages/cost of living index) * 100. Generally the list of items consumed varies for different classes of people (rich, middle, class, or the poor) at the same place of residence. Also people of the same class belonging to different geographical regions have different consumer habits. Thus the cost of living index always relates to specific class of people and a specific geographical area, and it help in determining the effect of changes in price on different classes of consumers living in different areas. The process of construction of cost of living index number is as follows

  1. Obtain decision about class of people for whom the index number is to be computed, for instance, the industrial personnel, officers or teachers etc. Also decide on the geographical area to be covered.

  2. Conduct a family budget inquiry covering the class of people for whom the index number is to be computed. The enquiry should be conducted for the base year by the process of random sampling. This would give information regarding the nature, quality and quantities of commodities consumed by an average family of the class and also the amount spent on different items of consumption.

  3. The item on which the information regarding money spent is to be collected are food (rice, wheat, sugar, milk, tea etc), clothing, fuel and lighting, housing and miscellaneous items.

  4. Collect retail prices in respect of the items from the localities in which the class of people concerned reside, or from the markets where they usually make their purchases.

  5. as the relative importance of various items for different classes of people is not the same, the price or price relative are always weighted and therefore, the cost of living index is always a weighted index.

  6. The percentage expenditure on an item constitutes the weight of the item and the percentage expenditure in the five groups constitutes the group weight.

  7. Separate index number are first of all determined for each of the five major groups, by calculating the weighted average of price-relatives of the selected items in the group.

Index Number Of Industrial Production

The index number of industrial production is designed to measure increase or decrease in the level of industrial production in a given period of time compared to some base periods. Such an index measures changes in the quantities of production and not their values. Data about the level of industrial output in the base period and in the given period is to be collected first under the following heads

  • Textile industries to include cotton, woolen, silk etc.
  • Mining industries like iron ore, iron, coal, copper, petroleum etc.
  • Metallurgical industries like automobiles, locomotive, aero planes etc
  • Industries subject to excise duties like sugar, tobacco, match etc.
  • Miscellaneous like glass, detergents, chemical, cement etc.


The figure of output for a various industries classifies above are obtained on a monthly, quarterly or yearly basis. Weights are assigned to various industries on the basis of some criteria such as capital invested turnover, net output, production etc. Usually the weights in the index are based on the values of net output of different industries. The index of industrial production is obtained by taking the simple mean or geometric mean of relatives. When the simple arithmetic mean is used the formula for constructing the index is as follows.

Index of industrial production = (100/w) * (q1/q0) * w = (100/w) * I * w

  • Where q1 = quantity produced in a given period
  • Q0 = quantity produced in the base period
  • W = relative importance of different outputs
  • I = (q1/q0) = index for respective commodity