Page 212 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 10: Index Number

Omitting the subscript i, the above index number can also be written as: Notes

p 1
P 01 100
p
0

Example: The following table gives the prices of six items in the years 2010 and 2011. Use
simple aggregative method to find index of 2011 with 2010 as base.
Price in Price in
Item
2010 ( ) 2011 ( )
A 40 50
B 60 60
C 20 30
D 50 70
E 80 90
F 100 100
Solution:
Let p be the price in 2010 and p be the price in 2011. Thus, we have
0 1
Sp = 350 and Sp = 400
0 1
400
P 01 100 114.29
350
4. Weighted Aggregative Method: This index number is defined as the ratio of the weighted
arithmetic means of current to base year prices multiplied by 100.
Using the notations, defined earlier, the weighted arithmetic mean of current year prices
p w i
1i
can be written as =
w
i
p w i
0i
Similarly, the weighted arithmetic mean of base year prices
w
i
p w i
1i
w p w
Price Index Number, P i 100 1i i 100
01
p w p w
0i i 0i i
w i
p w
Omitting the subscript, we can also write P 01 1 100
p w
0

Nature of Weights

In case of weighted aggregative price index numbers, quantities are often taken as weights.
These quantities can be the quantities purchased in base year or in current year or an average of
base year and current year quantities or any other quantities. Depending upon the choice of
weights, some of the popular formulae for weighted index numbers can be written as follows:

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