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Index numbers may be constructed by any of the following methods—

**(1) Unweighted Index : **

(a) Simple Aggregative Index

(b) Simple Average of Relatives

**(2) Weighted Indices:**

(a) Weighted Aggregative. Index

(b) Weighted Average of Relatives

**UNWEIGHTED INDEX : SIMPLE AVERAGE OF PRICE RELATIVE METHOD**

Under this method the price of each commodity in the current year is taken as a percentage of the price of corresponding item of the base year and the index is obtained by averaging these percentage figures.

Arithmetic mean or geometric mean may be used to average these percentages.

**When arithmetic mean is used **for averaging the relatives, the formula for computing the index is :

Where p_{1 }= price of current year

p_{0} = price of base year

N = Total Number of items

**When geometric mean is used** for averaging the relatives, the formula for computing the index is :

**Example 1 :**

From the following data construct an index for 2012 taking 2011 as base by Price Relative method using

(a) Arithmetic Mean

(b) Geometric Mean for averaging relatives:

**Solution : **Index Number using Arithmetic Mean of Price Relative

**Table : Calculation of Price Relatives of Arithmetic Mean**

To determine the value of a and b, the following two normal equations are to be solved simultaneously:

**Table : Calculation of Price Relatives of Geometric Mean**

**Note : **The difference in the answer is due to the method of averaging used.

**Unweighted Indices**

**(a) Simple Aggregate Method - This is the simplest method of construction index numbers. It consists of expressing the aggreate price of all commodities in the current year as a per cent of the aggregate price in the base year. Symbolically:**

Where Σp_{0} = total of prices of all commodities of base year

Σp_{1 }= total of prices of all commodities of current year

p_{01} = Index Number of current year

**Examples : 2 **From the following data construct a price Index for year 2012 taking year 2009 as base

**Solution : Table : Construction of Price Index**

This means that as compared to 2009, in 2012 there is a net increase in the prices of the given commodities to the extent of 36%.

This method has following limitations –

(1) The index is affected by the units in which the prices are quoted (such as litres, kilogram etc.). In the preceding example, if the prices of chese is taken in per kg (instead of as per 100 gms) e.g. 80 in 2009 and 100 in 2012 the index so computed would differ as follows :

Table : Construction of Price Index

The net increase in price now is only 29%.

(2) The relative importance of various commodities is not taken into account in as it is unweighted. Thus according to this method equal weights (importance) would be attached to wheat and salt in computing a cost of living index.

(3) This method is influenced by the magnitude of prices i.e. the higher the price of the commodity, the greater is the influence on the Index number. Such price quotations become the concealed weights which have no logical significance.

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