Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 7.15

Example 6 :
An enquiry into the budgets of the middle class families in a city in India gave the following information:
Food Rent Clothing Fuel Others
Expenses 35% 15% 20% 10% 20%
Price in 2011 150 50 100 20 60
Price in 2012 174 60 125 25 90

What change in the cost of living of 2012 has taken place as compared to 2011
Solution:
Table : Calculation of Cost of living
Items Expenses Price in Price in p =^10 ×^100

p

p PW

(%) W 2011 (p 0 ) 2012 (p 1 )

Food 35 150 174 115074 ×^100115074 ×^100 x 35 = 4060

Rent 15 50 60 6050 x 100^6050 x 100 x 15 = 1800

Clothing 20 100 125 125100 x 100^125100 x 100 x 20 = 2500

Fuel 10 20 25 2520 x 100^2520 x 100 x 10 = 1250

Others 20 60 90 9060 x 100^9060 x 100 x 20 = 3000

ΣW = 100 ΣPW= 12610

01

P PW 12,610 126.1

W 100

= Σ = =

Σ

The cost of living in 2012 has increased by 26.1% as compared to 2011.

7.8 TEST OF ADEQUACY OF THE INDEX NUMBER FORMULAE

So far we have discussed various formulae for construction of weighted & unweighted index numbers.
However the problem still remains of selecting an appropriate method for the construction of an index
number in a given situation. The following tests can be applied to find out the adequacy of an index
number.

(1) Unit Test

(2) Time Reversal Test

(3) Factor Reversal Test

(4) Circular Test