Paper 4: Fundamentals of Business Mathematics & Statistic

7.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Index Numbers

Group 2008 2009 2010 2011 2012

Total of Link Relatives 300 400 413.33 375 360

Average of Link Relatives 100 133.33 137.77 125 120

Chain Index 100 100 133.33× 100 133.33 137.77 100 × 183.69 125 100 × 229.69 120 100 ×

= 133.33 = 183.69 = 229.61 = 275.53

Table : Computation of Fixed base Index No.

Group 2008 2009 2010 2011 2012

I 100 96 x 100 =150^126 x 100 =200^156 x 100 =250^186 x 100 = 300

II 100 108 x 100 =125^128 x 100=150^158 x 100 =187.5^188 x 100 = 225

IIII 100 1512 x 100 =125 1224 x 100 =200^3012 x 100 =250 1236 x 100 =300

Total 300 400 550 687.5 825

AV 100 133.33 183.33 229.17 275

Note : The two series of index numbers obtained by fixed base & chain base method are different except in

the first two years. This would always be so in case of more than one series.

Example 10 :

The price index & quantity index of a commodity were 120 & 110 respectively in 2012 with base 2011. Find its

value index number in 2012 with base 2011.

Solution:

1 1

0 0

pp ×100 120=^ pp^ 1.2

1 1

0 0

qq ×100 110=^ qq^ 1.1

11

0 0

∴Value index=p qpq × 100

=1.2 1.1 100 132× × =

SELF EXAMINATION QUESTION

Problem I. Hence, factor reversal test is satisfied.

Problem 2. Explain the usefulness of constructing chain indices

Problem 3. Define Index Number. Explain the problems while constructing the Index No.

Problem 4. Discuss the problems faced while constructing an Index No.

Problem 5. Distinguish between fixed base Index and chain base Index Number.

Problem 6. Discuss the importance of cost of living index. What are the problems in construction of cost

of living Index?