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Quantitative Techniques – I

Notes
Figure 10.1: Various Methods of Index Number Construction

In addition to this, a particular method would depend upon the type of average used. Although,
geometric mean is more suitable for averaging ratios, arithmetic mean is often preferred because
of its simplicity with regard to computations and interpretation.

10.4 Notations and Terminology

Before writing various formulae of index numbers, it is necessary to introduce certain notations
and terminology for convenience.
Base Year: 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.
Current Year: The year under consideration for which the comparisons are to be computed is
called the current year. It is commonly denoted by writing ‘1’ as a subscript of the variable.
i
Let there be n items in a group which are numbered from 1 to n. Let p denote the price of the
0
i
th
i item in base year and p denote its price in current year, where i = 1, 2, ...... n. In a similar way
1
i
i
th
q and q will denote the quantities of the i item in base and current years respectively.
0 1
Using these notations, we can write an expression for price relative of the ith item as
p q 1i
P 1i 100 , and quantity relative of the i th item as Q i 100
i q
p 0i
0i
Further, P will be used to denote the price index number of period ‘1’ as compared with the
01
prices of period ‘0’. Similarly, Q and V would denote the quantity and the value index
01 01
numbers respectively of period ‘1’ as compared with period ‘0’.
10.5 Price Index Numbers
1. Simple Average of Price Relatives:
(a) When arithmetic mean of price relatives is used
p
1i 100
P p
The index number formula is given by P i or P 0i Omitting
01 01
n n
p
1 100
the subscript i, the above formula can also be written as P = p 0
01
n
(b) When geometric mean of price relatives is used
The index number formula is given by
 Antilog
( is used to denote the product of terms.)

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