Page 242 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
⎡ P ⎤
Antilog ∑ log ⎢ 1 × 100 ⎥
P 01 = N ⎣ P 0 ⎦

⎛ P ⎞
If ⎜ 1 × 100 ⎟ is represented by P, then
⎝ P 0 ⎠

∑ log P
P 01 = Antilog N

The following example will illustrate the application of above rules.
Example 2: In the above example 2, Calculate Index Number using Geometric Mean as Average
of Relatives.
Solution:

P 1
Commodities 1983 Base 1993 Current P = P 0 × 100 log P
Year Price Year Price
P 0 P 1

200
Wheat 100 200 × 100 = 200 2.3010
100

40
Ghee 8 40 × 100 = 500 2.6990
8
4
Milk 0.50 4 × 100 = 800 2.9031
0.5

800
Rice 200 800 × 100 = 400 2.6021
200
6
Sugar 1 6 × 100 = 600 2.7782
1
∑ logP = 13.2834

∑ logP
P
log 01 =
N
13.2834
log 01 =
P
5
log P 01 = Antilog [2.6567]

P 01 = 453.63

Example 3: From the following data construct an Index for 2005 taking 2004 as base by the average
of relatives methods using (a) arithmetic mean, and (b) geometric mean for averaging
relatives.

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