Paper 4: Fundamentals of Business Mathematics & Statistic

7.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

Solution:

Index Number using Arithmetic Mean of Price Relative

Table : Calculation of Price Relatives of Arithmetic Mean

Commodities Prices in 2011 Prices in 2012 Price Relatives

P 0 P 1 01

P p 100

=p ×

A 8 12 150

B 6 8 133.33

C 5 6 120

D 48 52 108.3

E 15 18 120

F 9 27 300

Σ P = 931.63

=Σ = =

01

P p 931.63 155.27%

N 6

To determine the value of a and b, the following two normal equations are to be solved simultaneously:

Table : Calculation of Price Relatives of Geometric Mean

Commodities p 0 p 1 p =^10 ×

p 100

p log P

A 8 12 150 2.1761

B 6 8 133.33 2.1249

C 5 6 120 2.0792

D 48 52 108.3 2.0346

E 15 18 120 2.0792

F 9 27 300 2.4771

Σlog P = 12.9711

P 01 = Antilog 12.9711 6

= Antilog 2.1618

= 145.1%

Note: The difference in the answer is due to the method of averaging used.

Unweighted Indices

(a) Simple Aggregate Method - This is the simplest method of construction index numbers. It consists of

expressing the aggreate price of all commodities in the current year as a per cent of the aggregate

price in the base year. Symbolically:

=Σ ×

Σ

01 1

0

P pp 100