Page 210 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 10: Index Number

Notes
Example: Given below are the prices of 5 items in 2005 and 2010. Compute the simple
price index number of 1990 taking 2005 as base year. Use (a) arithmetic mean and (b) geometric
mean.
Price in 2005 Price in 2010
Item
(Rs/unit) (Rs/unit)
1 15 20
2 8 7
3 200 300
4 60 110
5 100 130

Solution:
Calculation Table
Price Relative
Price in Price in
Item p 1i log P i
2005 (P ) 2010 (P ) P = p ×100
0i
i
0i
0i
1 15 20 133.33 2.1249
2 8 7 87.50 1.9420
3 200 300 150.00 2.1761
4 60 110 183.33 2.2632
5 100 130 130.00 2.1139
Total 684.16 10.6201

684.16
Index number, using A.M., is P 01 136.83
5
10.6201
and Index number, using G.M., is P 01 Antilog = 133.06
5
2. Weighted Average of Price Relatives: In the method of simple average of price relatives,
all the items are assumed to be of equal importance in the group. However, in most of the
real life situations, different items of a group have different degree of importance. In
order to take this into account, weighing of different items, in proportion to their degree
of importance, becomes necessary.
Let w be the weight assigned to the i th item (i = 1, 2, ...... n). Thus, the index number, given
i
Pw i
i
by the weighted arithmetic mean of price relatives, is P 01 .
w
i
Similarly, the index number, given by the weighted geometric mean of price relatives can
be written as follows:
1 1
w w w w w w
P P 1 .P 2  P n i P i i
01 1 2 n i
w log P
or P Antilog i i
01
w
i

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