Paper 4: Fundamentals of Business Mathematics & Statistic

7.18 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

2011 & another index for 2011 with the base of 2010. Then it should be possible for us to directly get an

index for the year 2012 with the base of 2010. If the index calculated directly does not give an inconsistent

value, the circular test is said to be satisfied.

This test is satisfied if—

P 01 x P 12 x P 20 = 1.

This test is satisfied only by the following index Nos. formulas—

(1) Simple aggregative index

(2) Simple geometric mean of price relatives

(3) Kelly’s fixed base method

When the test is applied to simple aggregative method—

∴ P 01 × P 12 × P 20 =

Σ ×Σ × Σ =

Σ Σ Σ

1 2 0

0 1 2

p p pp p p^1

Hence, the simple aggregative formula satisfies circular test

Similarly when it is applied to fixed weight Kelly’s method

Σ ×Σ × Σ =

Σ Σ Σ

1 2 0

0 1 2

p q pq p qpq p q p q^1

This test is not satisfied by Fishers ideal index.

Example7 :

Compute Fisher’s Ideal Index and show that it satisfies time Reversal Test

2009 2012

Items Price (`) Value (`) Price (`) Value (`)

A 10 30 12 48

B 15 60 15 75

C 5 50 8 96

D 2 10 3 15

Solution:

As in this problem value of each item is given we have to find out quantity by dividing the value by the

price. Symbolically :

Value = Price x Quantity

∴ Quantity = ValuePrice