Page 224 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 10: Index Number

Self Assessment Notes

State whether the following statements are true or false
18. Index numbers where comparisons of various periods were done with reference to a
particular period, termed as base period.

19. There is no problem with a fixed base series even when the base year becomes too distant
from the current year.
20. When there is a single commodity, the chained index will be equal to the fixed base index.

Case Study Cost of Living Index
A n enquiry into the budgets of middle class families of certain city revealed that,
on an average, the percentage expenses on the different groups were as follows:

Food 45, Rent 15, Clothing 12, Fuel and Light 8, Miscellaneous 20.
The group index numbers for the current year as compared to a fixed base were 410, 150,
343, 248 and 285 respectively. Calculate the cost of living index for the current year.

Mr. X was getting 240 in the base year and 430 in current year. State, how much he ought
to have received as extra allowance to maintain his former standard of living.

10.11 Summary

An index number is a statistical measure used to compare the average level of magnitude
of a group of distinct but related variables in two or more situations.
In real situations, neither the prices of all the items change in the same ratio nor in the
same direction, i.e., the prices of some commodities may change to a greater extent as
compared to prices of other commodities.

The index numbers are very useful device for measuring the average change in prices or
any other characteristics like quantity, value, etc., for the group as a whole.
Index numbers are specialized type of averages that are used to measure the changes in a
characteristics which is not capable of being directly measured.
The changes in magnitude of a group are expressed in terms of percentages which are
independent of the units of measurement. This facilitates the comparison of two or more
index numbers in different situations.
Index numbers are indispensable tools for the management of any government or non-
government organizations.
There is inverse relation between the purchasing power of money and the general price
level measured in terms of a price index number.
The reciprocal of the relevant price index can be taken as a measure of the purchasing
power of money.

The year from which comparisons are made is called the base year. It is commonly denoted
by writing ‘0’ as a subscript of the variable.

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