Paper 4: Fundamentals of Business Mathematics & Statistic

7.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

When Arithmetic Mean is used for averaging weighted relatives the formula is :

= Σ

(^01) Σ

P PV

V

where P =^10 ×^100

p

p

V = p 0 q 0

When Geometric Mean is used for averaging weighted relatives the formula is :

= Σ × ×

(^01) Σ
P antilog (logP V) 100
V
where P =^10 ×^100
p
p
V = p 0 q 0
Example 4 :
Compute price index by Weighted Average of Relatives using—
(1) Arithmetic mean
(2) Geometric mean
Items Price in 2011 Price in 2012 Quantity in 2011
A 5 6 2
B 4 5 0.25
C 15 16.5 1
Solution:
Table : Computation of price index using arithmetic mean
Items p 0 p 1 q 0 P =^10 ×^100
p
p V= p^0 q^0 PV
A 5 6 2 65 ×100 120= 10 1200
B 4 5 0.25 45 ×100 125= 1 125
C 15 16.5 1 16.5 15 ×100 110= 15 1650
ΣV = 26 ΣPV = 2975
01

P PV

V

2975

26

= Σ

Σ

=

P 01 = 114.42