Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.19

Table : Calculation of Fisher’s Ideal Index

2009 2012

Item Price (`) Value (`) Price (`) Value (`) q 0 = q 1 = p 0 q 1 p 1 q 0

p 0 p 0 q 0 p 1 p 1 q 1 0 0

0

p q

p

1 1

1

pq

p

A 10 30 12 48 3 4 40 36

B 15 60 15 75 4 5 75 60

C 5 50 8 96 10 12 60 80

D 2 10 3 15 5 5 10 15

Σp 0 q 0 =150 Σp 1 q 1 =234 Σp 0 q 1 =185 Σp 1 q 0 =191

01 1 0^11

0 0 0 1

P = ΣΣp q p qpq × ΣΣpq × 100

19 1 234 100 1.273 1.265 100

= 150 185× × = × ×

= 1.6039 100×

=1.2691 100 126.91× =

Time reversal test is satisfied when
P 01 x P 10 = 1

01 10 1 0 1 1 0 1 0 0

0 0 0 1 1 1 1 0

P P× = ΣΣp q p qpq × ΣΣpq × ΣΣp q p qpq pq× ΣΣ

191 234 185 150

= 150 185 234 191× × ×

191 234 185 150

= 150 185 234 191× × ×

= 1 1=

Since P 01 x P 10 = 1 hence Fisher’s ideal index satisfies time Reversal Test.

7.9 CHAIN INDEX NUMBERS

In the fixed base method which is discussed so far the base remains the same & does not change whole
throughout the series. But with the passage of time some items may have been included in the series &
other ones might have been deleted, & hence it becomes difficult to compare the result of present conditions
with those of the old remote period. Hence the fixed base method does not suit when the conditions
change. In such a case the changing base period may be more suitable. Under this method the figures for
each year are first expressed as a percentage of the preceding year (called link relatives) then they are
chained together by successive multiplication to form a chain index.