Although index numbers are indispensable tools in economics, business, management etc, they have their limitations and proper care should be taken while interpreting them. Some of the limitations of index numbers are as given below:
1. Not based on all items: Since index numbers are generally based on a sample, it is not possible to take into account each and every item in the construction of index.
2. Not free from Error: At each stage of the construction of index numbers, starting from selection of commodities to the choice of formulae there is a chance of the error being introduced. Index numbers are also special type of averages, since the various averages like mean, median, GEOMETRICMEAN have their relative limitations, their use may also introduce some error. None of the formulae for the construction of index numbers is exact and contains the so called formula error. For example Laspayer's index number has an upward bias while Paasche's index has a downward bias.
3. Meant for Particular Purpose: An index number is used to measure the change for a particular purpose only. Its misuse for other purposes would lead to unreliable conclusions.
4. Difference of Time: With the passage of time, it is difficult to make comparisons of index numbers. Over time a person's habit, taste etc. Also undergo change. Consequently, index numbers constructed on the basis of old consumption pattern and hence it becomes obsolete over time. In the construction of price or quantity index numbers it may not be possible to retain the uniform quality of commodities during the period of investigation.
5. Difficulty in getting data on retail prices: Retail prices vary a great deal from place to place. Most of the index numbers are prepared on the basis of wholesale prices.
6. International Comparison is not Possible: Different countries develop their indices different years as base years and hence inter-country comparison is not possible by using international comparison.

The index number of industrial production aims to measure the change in the level of industrial production in a given period as compared to some other time period which is called base year. It measures changes in the quantity of output instead of change in its money value. In India these statistics are compiled by official and non-official agencies. The general index of industrial production is most popular among these. In India, index of industrial production is published by Central Statistical Organization (CSO), Industrial Statistics Wing. In computing an index of industrial production as a whole the area which is to be covered needs to be defined properly. These indices are limited to secondary sector activities. Building and construction are also taken as doubtful items at times. A more difficult problem arises in case of repair work. Some repair work is clearly a part of secondary sector like repairs in shipbuilding or railways but sometimes repair is a part of service sector like automobile repairs, shoe repairs, cloth repairs etc. Another problem arises in selection of weights: some use quantity as weights while others use value as weights. Usually, important data about production are collected under the following major heads.
(a) Mining Industries-Coal, Iron Ore, Copper, Aluminium, Petroleum etc.
(b) Metallurgical Industries- Iron and Steel, Steel Industry etc.
(c) Mechanical Industries: Locomotives, ships, aero planes etc.
(d) Textile Industries- Cotton, Woolen, Jute, Silk etc.
(e) Industries subject to Excise Duty- Sugar, tobacco" Breweries, Tobacco etc.
(f) Miscellaneous-Cement, Glass, Soap, Chemical etc. The table given below shows broad industrial groupings and their weights

Usually eights in a index number of industrial production are based on the net output of various industries. The weighted arithmetic mean or geometric mean of the relatives gives the index number of industrial production. Such index numbers can be constructed for gross output as well as net output. Index Number of Industrial Production
(IIP)=\(\frac { \sum { \left( \frac { { q }_{ 0 } }{ { q }_{ 1 } } \right) } }{ \sum { W } } \)
Where q₁= Current Year Quantity Produced
q₀ = Base Year Quantity Produced
W= Relative importance of different outputs

The Wholesale price Index measures the relative changes in the prices of commodities traded in the wholesale markets. These are constructed on weekly basis. These are published every week by the office of Economic Advisor, ministry of Industry, Government of India. First, such index number was constructed in 1947 and thereafter in 1952-53 as base year in 1956. In India, 2004-05 is used as base year for constructing index numbers.
(a) Forecasting Demand and Supply: The wholesale price indices are often used to forecast demand and supply situation in the economy. By considering present demand and supply situation, we can have an idea of demand and supply in the future.
(b) Forecasting Future prices: By looking at WPI statistics of an economy or a state, one can have an idea of expected price rise in the future.
(c) Determination of Real Changes in Aggregates: The wholesale price index enables us to find out the real changes in aggregates like national income and national expenditure. It can be understood by looking at the formula of estimating real national income from nominal national income. Real Change in National Income = 0 It is clear from above that given Wholesale price index we can convert nominal aggregates into real aggregates which are free from the effect of price changes.
(d) Indicator of Rate of Inflation: Te wholesale price index is also used to find the rate of inflation in an economy in a financial year or other time period.
Rate of Inflation
\(\frac{current year WPI-Previous year WPI}{Previous Year WPI}\times 100\)
Wholesale price index is prepared every week. If suppose WPI for week 1 is 400 and for week 2 it is 450 then rate of inflation will be equal to:
Rate of Inflation
\(\frac{450-400}{400}\times100\) =12.5%
(e) Useful in Planning: Government launches many plans which require huge amount of expenditure and take a long time in their completion. It is difficult to estimate the cost of their construction without availability of WPI. Government needs to make provision for these in its five year plans. It is useful in finding the real cost of producing these goods and services. Government also needs to know rate of inflation for making efficient plans and to allocate resources amongst different schemes and sectors of the economy.

The Fisher's index number is called ideal index number due to the following characteristics.
(a) It is based on the GEOMETRIC MEAN which is theoretically considered as the best average of constructing index numbers.
(b) It takes into account both current and base year prices as quantities.
(c) It satisfies both time reversal and factor reversal test which are suggested by Fisher.
(d) The upward bias of Lasperey's index number and downward bias of Paasche's index number are balanced to a great extent.
(e) Irving Fisher has considered two important properties which an index number should satisfy. These are tests of reversibility.
Time reversal test
Factor reversal test
If an index number satisfies these two tests it is said to be an ideal index number. Fisher's formula satisfies both these tests. (You will read about these tests in detail in higher classes.)

The term weight refers to the relative importance of the different items in the construction of the index. Generally various items say wheat, rice, kerosene, clothing etc. included in the index are not of equal importance, proper weights should be attached to them to take into their relative importance. Thus there are two types of indices.
1. Unweighted indices-in which no specific weights are attached to various commodities.
2. Weighted indices-in which appropriate weights are assigned to various commodities. The Unweighted indices can be interpreted as weighted indices by assuming the corresponding weight for each commodity being unity. But actually the commodities included in the index are all not of equal importance. Therefore it is necessary to adopt some suitable method of weighting, so that arbitrary and haphazard weights may not affect the results.
There are two methods of assigning weights.
(i) Implicit weighting
(ii) Explicit weighting In implicit weighting, a commodity or its variety is included in the index a number of times. For example if wheat is to be given in an index twice as much times as rice then the-weight of wheat is two whereas in explicit weighting two types of weights can be assigned. i.e. quantity weights or value weights. A quantity weight symbolized by q means the amount of commodity produced, distributed or consumed in some time period. A value weight in the other hand combines price with quantity produced, distributed or consumed and is denoted by v = PQ. For example quantity weights are used in the method of weighted aggregative like Lasperey's, Paasche's index numbers and value weights are used in the method of weighted average of price relatives.

"In its simplest form an index number is the ratio of two index numbers expressed as a per cent. An index number is a statistical measure-a measure designed to show changes in one variable or in a group of related variables over time, or with respect to geographic location, or in terms of some other characteristics." - Patterson "An index number is a statistical measure designed to show changes in a variable or a group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc." - Spiegel Before constructing index numbers the careful thought must be given into following problems
1. Purpose of index numbers: An index number which is properly designed for a purpose can be most useful and powerful tool. Thus the first and the foremost problem are to determine the purpose of index numbers. If we know the purpose of the index numbers we can settle some related problems. For example if the purpose of index number is to measure the changes in the production of steel, the problem of selection of items is automatically settled. But the problem is index which is constructed for one purpose cannot be used of another purpose. Therefore, every time we have to reconstruct it for different purposes. For example, retail prices are meaningful in construction of consumer price index while wholesale prices are used for wholesale price index.
2. Selection of commodities: After defining the purpose of index numbers, select only those commodities which are related to that index. For example if the purpose of an index is to measure the cost of living of low income group we should select only those commodities or items which are consumed by persons belonging to this group and due care should be taken not to include the goods which are utilized by the middle income group or high income group i.e. the goods like cosmetics, other luxury goods like scooters, cars, refrigerators, television sets etc. Selection of items also get changes as soon as the purpose of index changes.
3. Selection of base period: The period with which the comparisons of relative changes in the level of phenomenon are made is termed as base period. The index for this period is always taken as 100.
4. Data for index numbers: The data, usually the set of prices and of quantities consumed of the selected commodities for different periods, places etc. constitute the raw material for the construction of index numbers. The data should be collected from reliable sources such as standard trade journals, official publications etc. for example for the construction of retail price index numbers, the price quotations for the commodities should be obtained from super bazaars, departmental stores etc. and not from wholesale dealers. Wherever we get data, e must ensure that it is reliable, accurate, adequate and comparable.
5. Price Quotations: Prices of many commodities vary from place to place. It is practically not possible to collect price quotations from all places. Therefore, we can use such areas which are well known for those commodities. There are two ways in which prices may b quoted:
(i)Money Prices: In this prices are quoted per unit of commodity like Rs.30 per kg 
(ii)Quantity prices: Quantity prices are quoted per unit of money. For example 50 ML milk per 1 rupee.
6. Selection of appropriate weights: A decision as to the choice of weights is an important aspect of the construction of index numbers. The problem arises because all items included in the construction are not of equal importance. Therefore, proper weights should be attached to them to take into account their relative importance. Thus there are two types of indices.
(a) Unweighted indices- in which no specific weights are attached
(b) Weighted indices- in which appropriate weights are assigned to various items.
7. Choice of average: Since index numbers are specialized averages, a choice of average to be used in their construction is of great importance. Usually the following averages can be used.
1. Arithmetic Mean
2. Geometric Mean
3. Median Among these averages Geometric Mean is the appropriate average to be used. But in practice Geometric Mean is not used as often as Arithmetic Mean because of its computational difficulties. Median has erratic difficulties.
8. Choice of formula: A large variety of formulae are available to construct an index number. The problem very often is that of selecting the appropriate formula. The choice of the formula would depend not only on the purpose of the index but also on the data available.

'Index numbers are devices for measuring differences in the magnitude of a group of related variables.- Croxton & Cowden Index numbers are indispensable tools of economics and business analysis. Following are the main uses of index numbers.
1. Index numbers helps in formulating suitable economic policies and planning: Many of the economic and business policies are guided by index numbers. For example while deciding the increase of DA of the employees; the employer's 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. The index numbers provide some guide lines that one can use in making decisions.
2. They are used in studying trends and tendencies: Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. For example for last 8 to 10 years we can say that imports are showing upward tendency.
3. Useful to Business Community: Businessmen need to know the trends in the market to take decisions about wage rates, prices of the product, prices of raw materials etc. Therefore, index numbers are very useful for them.
4. Information Regarding Foreign Trade: Index of Exports and Imports provides relevant information regarding foreign trade and accordingly government can formulate its export-import policy, business men who are engaged in foreign trade can take their decisions and one can predict changes in inflow or outflow of foreign exchange.
5. They are useful in forecasting future economic activity: Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity. Index numbers measure the purchasing power of money.
6. The cost of living index numbers determine whether the real wages are rising or falling or remain constant: The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. Real wages helps us in determining the purchasing power of money. Index numbers are used in deflating. Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers.
7. Used in Deflating: Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from Rs.10/ kg in the year 1980to Rs.20/kg in the year 1982. then a person can buy only half kilo of rice with Rs.10. so the purchasing power of a rupee is only 50 paise in 1982 as compared to 1980.
Thus the purchasing power of money|
\(\frac{1}{price index}\)
In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position.
For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100.
i.e \(\frac{Money wages}{price index}\times100\)
Thus Real wage index
=\(\frac{real wage of current year}{Real wage of base year}\times100\)

Obviously change in prices is reflected in price index numbers. It is the most important use of price indices to measure the value of money during different time periods. We take pO as base year price and PI as current year price and it is reflected in index numbers.

We need an index number because:
Index numbers are indispensable tools of economics and business analysis.
Following are the main uses of index numbers.
1. Index numbers are used as economic barometers: Index number is a special type of averages which helps to measure the economic fluctuations on price level, money market, economic cycle like inflation, deflation etc.
2. They are useful in forecasting future economic activity: Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity. Index numbers measure the purchasing power of money. Index of Exports and Imports provides relevant information regarding foreign trade and accordingly government can formulate its export-import policy, business men who are engaged in foreign trade can take their decisions and one can predict changes in inflow or outflow of foreign exchange.
3. The cost of living index numbers determine whether the real wages are rising or falling or remain constant: The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. Real wages helps us in determining the purchasing power of money. Index numbers are used in deflating. Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers.
4. Used in Deflating: Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from Rs.10/ kg in the year 1980to Rs.20/kg in the year 1982. then a person can buy only half kilo of rice with no. so the purchasing power of a rupee is only 50paise in 1982 as compared to 1980.
Thus the purchasing power of money \(=\frac { 1 }{ Price\quad Index } \) In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position.
For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100. 
Money wages i.e. Real wages = \(\\ \frac { Money\quad wages }{ Priceindex } \times 100\) 
Thus Real Wage Index \(=\frac { Realwagescurrentyear }{ Realwagesofbaseyear } \times 100\)
5. Index numbers helps in formulating suitable economic policies and planning: Many of the economic and business policies are guided by index numbers. For example while deciding the increase of DA of the employees; the employer's 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. The index numbers provide some guide lines that one can use in making decisions.
6. They are used in studying trends and tendencies: Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. For example for last 8 to 10 years we can say that imports are showing upward tendency. Businessmen need to know the trends in the market to take decisions about wage rates, prices of the product, prices of raw materials etc. Therefore, index numbers are very useful for them.

Given below are uses of consumer price index.
(a) Indicator of fall or rise in prices: Cost of living index numbers indicate whether the real wages are rising or falling. In other words they are used for calculating the real wages and to determine the change in the purchasing power of money.
Purchasing power of money
=\(\frac { 1 }{ costoflivingindexnumber } \)
Real Wages
=\(\frac { Moneywages }{ costoflivingindexnumber } \times 100\)
(b) Used for determining D.A.: Cost of living indices are used for the regulation of D.A or the grant of bonus to the workers so as to enable them to meet the increased cost of living.
(c) Used in Wage Negotiations: Cost of living index numbers are used widely in wage negotiations.
(d) Used in Market Analysis: These index numbers also used for analyzing markets for particular kinds of goods.