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The construction of an index number is not an easy task. Various problems hamper the construction of index number such as; what should be the base year, which commodities should be included, how should the weights allocated to each commodity etc. These are some of the problems which make it difficult to construct an index number on regular basis. The important problems of index number are discussed below.

### Defining Purpose

In the construction of index number, the defining purpose is the important step and indicates the purpose of measure to be calculated. Since the choice of weights, commodities, and base year all depend on the purpose of measure therefore it is necessary to define it before the construction of an index number.  For example we are constructing two indices i-e. cost of living index and whole sale price index. Here the weights, commodities, and base year of cost of living index will be totally different from the weights, commodities, and base year of whole sale price index.

### Commodities to be included

Selection of the commodities is an important problem in the construction of index number. The commodities should be relevant, comparable, representative and reliable. For example if we are measuring the cost of living of a particular class then only those commodities should be included which are consumed by the class. Similarly most common or most popular commodities should be used and the quality of these commodities should not vary from each other.

### Determination of weights

When the selection process of commodities is completed, the next step is the determination of weights to each commodity. The determination of weights depends upon the relative importance attached to each commodity. But the importance of a commodity varies with place, time and the habits of those who use or trade in it. Similarly it is also important to decide whether to keep the weights constant or change it periodically. Generally weights are kept constant over a long period of time to facilitate the comparisons.

### Collection of Prices

Collection of prices is also an important problem for the construction of index number. It requires a lot of time and financial resources to collect the information about actual prices on regular basis. For example an index number of people living in villages cannot be constructed with out collecting the prices from retail shops located in villages. Similarly it requires huge human and financial resources to collect the information of hundred of commodities from every major market from time to time.

### Choice of base Year

A base year should be a normal year, because it is the year to which all other are compared. The base year should be free from all hazards that affect the economy of the country e.g. floods, wars, earth quakes etc. If such things happen in a year then the economy of country will be effected which will ultimately effect the prices in the year. Now because the year is not a normal year therefore it cannot be taken as base year. It is therefore necessary to take care while selecting the base year. There are two types of base year.

• Fixed Base Year

It is the year which remains fixed for the comparison of prices of all years. For example 2005 is taken as base year for the comparison of prices of 2006, 2007, and 2008, Now because the prices of the three years are compared with the prices of 2005; therefore 2005 is the base year. The index of base year is 100. It shows that if the index of 2008 is 130 then there is an increase of 30% in prices as compared to base year (2005).

•  Chain Base Year

It is the year which does not remain fixed for the comparison of prices of all years. In case of chain base year every preceding year is taken as base year for every proceeding year. For example 2005 is taken as base year for 2006 and 2006 is taken as base year for 2007 similarly 2007 is taken as base year for 2008 and so on.

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