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,

p_{1} - current
year price

p_{0} - base year price

q_{1} - current
year quantity

q_{0} - 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.

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

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

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