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# Weighted Index Number

In general, all the commodities cannot be given equal importance, so we can assign weights to each commodity according to their importance and the index number computed from these weights are called as weighted index number.

Weighted Index Number

In general, all the commodities cannot be given equal importance, so we can assign weights to each commodity according to their importance and the index number computed from these weights are called as weighted index number. The weights can be production, consumption values. If ‘w’ is the weight attached to a commodity, then the price index is given by,

Let us consider the following notations,

p1 -    current year price

p0 - base year price

q1  -    current year quantity

q0  - base year quantity

where suffix ‘0’ represents base year and ‘1’ represents current year.

Note

To get exact Fisher’s price index number, one should use formula method rather than using

In Laspeyre’s price index number, the quantity of the base year is used as weight.

In Paasche’s price index number, the quantity of the current year is used as weight.

Example 9.10

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Solution

Laspeyre’s price index number

On an average, there is an increase of 16.60 % in the price of the commodities when the year 2000 compared with the year 2010.

Paasche’s price index number

On an average, there is an increase of 18.12 % in the price of the commodities when the year 2000 compared with the year 2010.

Fisher’s price index number

On an average, there is an increase of 17.36 % in the price of the commodities when the year 2000 compared with the year 2010.

Example 9.11

Construct the Laspeyre’s , Paasche’s and Fisher’s price index number for the following data. Comment on the result.

Solution

On an average, there is an increase of 29.52 % , 25.48% and 27.48% in the price of the commodities by Laspeyre’s, Paasche’s, Fisher’s price index number respectively, when the base year compared with the current year.

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12th Business Maths and Statistics : Chapter 9 : Applied Statistics : Weighted Index Number | Definition, Solved Example Problems | Applied Statistics