Paper 4: Fundamentals of Business Mathematics & Statistic

7.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

Disadvantage

This method does not take into account the weight of either the base year or the current year.

Example 3 :

Compute the price index as per the following methods:

(1) Laspeyres’

(2) Paasche’s

(3) Fisher

(4) Bowley’s

(5) Marshall - Edgeworths

from the following :

Item p 0 q 0 p 1 q 1

A 10 4 12 6

B 15 6 20 4

C 2 5 5 3

D 4 4 4 4

Solution:

Table : Calculation of various indices

p 0 q 0 p 1 q 1 p 0 q 0 p 0 q 1 p 1 q 0 p 1 q 1

A 10 4 12 6 40 60 48 72

B 15 6 20 4 90 60 120 80

C 2 5 5 3 10 6 25 15

D 4 4 4 4 16 16 16 16

Σp 0 q 0 =156 Σp 0 q 1 =142 Σp 1 q 0 =209 Σp 1 q 1 =183

(i) Laspeyres’ Index Number

=Σ ×

Σ

= × =

01 1 0

0 0

P 100

(^209) 100 133.97
156
p q
p q
(ii) Paasche’s Index Number
01 1 1
0 1

P 100

(^183) 100 128.87
142
p q
p q

=Σ ×

Σ

= × =