Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.9

(iii) Bowley’s Index Number

Σ + Σ

=Σ Σ ×

+

= ×

= + ×

= × =

1 0 1 1

P 01 0 0 0 1 100

2

209 183

156 142 100

2

1.34 1.29 100

2

2.63 100 131.5

2

pq pq

p q p q

(iv) Fisher’s Index Number

= Σ × Σ ×

Σ Σ

01 1 0 1 1

0 0 0 1

P p q p qpq pq 100

= 209 183156 142× × 100

=^3824722152 × 100

= 1 726 100 1 31 100⋅ × = ⋅ ×

= 131

(v) Marshall-Edgeworth Index Number

= Σ + ×

Σ +

01 1 0^1

0 0 1

P ( ) 100

( )

p q q

p q q

1 0 1 1

0 0 0 1

= ΣΣp q p qp q p q+ Σ+ Σ × 100

= + ×

+

209 183 100

156 142

(^382) 100 131.54
= 298 × =
7.3.3 Weighted Index : Weighted Average of Relative Method
In this method price of each commodity in the current year is taken as a percentage of the price of
corresponding item of the base year. These relatives are multiplied by the given weights and the result is
obtained by averaging the resulting figures. Arithmetic mean or geometric mean is used to average these
figures.