7.12 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

= Σ

(^01) Σ

P PV

V

=36224.1316.5 =114.45

7.4 QUANTITY INDEX NUMBERS

Just as the price index number measures the changing prices of the goods so a quantity index number

measures the change in quantity/volume of the goods produced, sold or consumed. The method of

construction of quantity index number are similar to the methods discussed above in the context of price

index. The only difference is that the quantity index formula are obtained from the corresponding price

index formula by an interchange of p by q & q by p.

Thus the following list of formulae can be derived :

Unweighted Index : Simple Aggregative Method

= Σ ×

Σ

01 1

0

Q qq 100

Unweighted Index : Simple Average of Quantity Relative Method

• When Arithmetic Mean is used for averaging the relatives

Σ^ ×^

(^)

1
01 0

100

Q N

q

q

• When Geometric Mean is used for averaging the relatives

Σ^ ×^

(^)

1
01 0
log 100
Q antilog N
q
q
Weighted Index : Simple Aggregative Method

• Laspeyres’ Method

= Σ ×

Σ

01 1 0

0 0

Q q pq p 100

• Paasche’s Method

= Σ ×

Σ

01 1 1

0 1

Q q pq p 100

• Dorbish & Bowley’s Method
  Σ +Σ
  = Σ Σ ×

1 0 1 1

Q 01 0 0 0 1 100

2

q p q p

q p q p