Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.7

= Σ ×

Σ

01 1 1

0 1

P pqp q 100

Dorbish and Bowley’s Method
This method is the simple arithmetic mean of the Laspeyres’ and Paasche’s indices. This index takes into
account the influence of quantity weights of both base period and current period. The formula is as follows:

1 0 1 1

P 01 0 0 0 1 100

2

pq pq

p q p q

Σ + Σ

= Σ + Σ ×

Fisher ‘Ideal’ Method
This method is the geometric mean of Laspeyres’ and Paasche’s indices. The formula is as follows—

= Σ × Σ ×

Σ Σ

01 1 0 1 1

0 0 0 1

P p q p qpq pq 100

Advantages
Because of the following advantages this method is seldom referred as ideal method—
(1) The formula takes into account both base year and current year quantities as weights, and hence
avoids bias associated with the Laspeyres’ and Paasche’s indices.
(2) The formula is based on geometric mean which is considered to be the best average for constructing
index numbers.
(3) This method satisfies unit test, time reversal test and factor reversal test.
Disadvantage
(1) This method is more time consuming than other methods.
(2) It also does not satisfy circular test.
Marshall-Edgeworth Method
In this method arithmetic mean of base year and current year quantities are taken as weights symbolically—

Σ^ +^

(^)
= + ×
Σ (^)
1 1 2
(^0112)
0

P^2100

2

p q q

p q q

Kelly’s Method
In this method fixed weights are taken as weights. This method is sometimes referred to as aggregative
index with fixed weights method. Fixed weights are quantities which may be for some particular period (not
necessarily of base year or the current year) and this is kept constant all the time. The formula is as follows—

= Σ ×

Σ

01 1

0

P p qp q 100

Advantage
(1) This index does not require yearly changes in the weights.