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Index Numbers — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsIndex Numbers6 Marks
Question
Discuss in brief, the methods of constructing weighted index numbers.
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Answer

Weighted index numbers are the index number in which different items of the series are accorded different weightage, depending upon their relative importance.There are two methods of constructing weighted index numbers:
  1. Weighted Average of Price Relative Method: According to this method, weighted index number is simply the weighted arithmetic mean of price relative. In this method, weighted sum of the price relative is divided by the sum total of the weights.
$\text{Thus,}\ \text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}$
  1. Weighted Aggregative Method: Under this method, weights are assigned to various items and instead of finding the simple aggregate of price, the weighted aggregate of the price are obtained. The different methods to compute weighted aggregative index numbers are:
Laspeyre's Method: This method uses the base year quantities as weights. The following formula is used to calculate index number
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100$
Paasche's Method: This method uses the current year quantities as weights The following formula is used to calculate index number
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\text{p}_0\text{q}_1}\times100$
Fisher's Method: This method combines the techniques of Laspeyre's method and Paasche's method and uses both base year as well as current year quantities $(q_0, q_1)$ as weight.
The formula to construct index number is:
$\text{P}_{01}=\sqrt{\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}}\times100$

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