FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.3

Index Numbers

Unweighted Weighted

Simple Simple average Weighted Weighted

aggregate of price relative aggregate average of

price relatives

7.3.1 UNWEIGHTED INDEX : SIMPLE AVERAGE OF PRICE RELATIVE METHOD

Under this method the price of each commodity in the current year is taken as a percentage of the price of
corresponding item of the base year and the index is obtained by averaging these percentage figures.
Arithmetic mean or geometric mean may be used to average these percentages.
When arithmetic mean is used for averaging the relatives, the formula for computing the index is :

1

01 0

p 100

P p

N

(^) ×
(^)

Where p 1 = price of current year
p 0 = price of base year
N = Total Number of items
When geometric mean is used for averaging the relatives, the formula for computing the index is :
(^) ×
(^)

(^10)
01
log p 100
P Antilog p
N
Example 1 :
From the following data construct an index for 2012 taking 2011 as base by Price Relative method using
(a) Arithmetic Mean
(b) Geometric Mean
for averaging relatives:
Commodities Price in 2011 Price in 2012
A 8 12
B 6 8
C 5 6
D 48 52
E 15 18
F 9 27