Page 208 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 10: Index Number

10.3 Construction of Index Numbers Notes

To illustrate the construction of an index number, we reconsider various items of food mentioned
earlier. Let the prices of different items in the two years, 1990 and 1992, be as given below:

Price in 2009 Price in 2011
Item
(in /unit) (in /unit)
1. Wheat 300/quintal 360/quintal
2.Rice 12/kg. 15/kg.
3.Milk 7/litre 8/litre
4.Eggs 11/dozen 12/dozen
5.Ghee 80/kg. 88/kg.
6.Sugar 9/kg. 10/kg.
7. Pulses 14/kg. 16/kg.

The comparison of price of an item, say wheat, in 1992 with its price in 1990 can be done in two
ways, explained below:
1. By taking the difference of prices in the two years, i.e., 360 – 300 = 60, one can say that the
price of wheat has gone up by 60/quintal in 1992 as compared with its price in 1990.

360
2. By taking the ratio of the two prices, i.e., 1.20 , one can say that if the price of wheat
300
in 1990 is taken to be 1, then it has become 1.20 in 1992. A more convenient way of
comparing the two prices is to express the price ratio in terms of percentage, i.e.,
360
100 120 , known as Price Relative of the item. In our example, price relative of
300
wheat is 120 which can be interpreted as the price of wheat in 1992 when its price in 1990
is taken as 100. Further, the figure 120 indicates that price of wheat has gone up by 120 – 100
= 20% in 1992 as compared with its price in 1990.
The first way of expressing the price change is inconvenient because the change in price depends
upon the units in which it is quoted. This problem is taken care of in the second method, where
price change is expressed in terms of percentage. An additional advantage of this method is that
various price changes, expressed in percentage, are comparable. Further, it is very easy to grasp
the 20% increase in price rather than the increase expressed as 60/quintal.
For the construction of index number, we have to obtain the average price change for the group
in 1992, usually termed as the Current Year, as compared with the price of 1990, usually called
the Base Year. This comparison can be done in two ways:
1. By taking suitable average of price relatives of different items. The methods of index
number construction based on this procedure are termed as Average of Price Relative
Methods.

2. By taking ratio of the averages of the prices of different items in each year. These methods
are popularly known as Aggregative Methods.
Since the average in each of the above methods can be simple or weighted, these can further be
divided as simple or weighted. Various methods of index number construction can be classified
as shown below:

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