Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.11

Computation of Price Index using geometric mean

Items p 0 p 1 q 0 P = 01 ×^100

p

p V = p^0 q^0 logP V x log P

A 5 6 2 120 10 2.0792 20.792

B 4 5 0.25 125 1 2.0969 2.0969

C 15 16.5 1 110 15 2.0414 30.621

ΣV = 26 Σlog PV =

53.5099

= Σ ×

(^01) Σ
P antilog logP V
V
=antilog53.5099 26
=antilog 2.0581
=114.3
Example 5 :
The following table gives the prices of some food items in the base year & current year & the quantities sold
in the base year. Calculate the weighted index number by using the Weighted Average of Price Relatives:
Items Base year quantities Base year Price Current year Price
(units) (in ) (in)
A 7 18.00 21
B 6 3.00 4
C 16 7.50 9
D 21 2.50 2.25
Solution:
Table : Calculation of Weighted Average of Price Relation
Item Base year Base year Current P =^10 ×^100
p
p V = p^0 q^0 PV
quantities Price Price
q 0 p 0 p 1
A 7 18 21 1821 x 100 = 116.66 18 x 7 =126 14699.16
B 6 3 4 43 x 100 =133.33 6 x 3 =18 2399.94
C 16 7.5 (^9) 7.5^9 x 100 =120 16 x 7.5 =120 14400
D 21 2.5 2.25 2.252.5 x 100 = 90 21X2.5 = 52.5 4725
ΣV = 316.5 ΣPV=36224.1