Page 241 - DMGT404 RESEARCH_METHODOLOGY

Unit 11: Index Numbers

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

Notes 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.
Let there be n items in a group which are numbered from 1 to n. Let p denote the price of
0i
the i th item in base year and p denote its price in current year, where i = 1, 2, ...... n. In a
1i
similar way q and q will denote the quantities of the i th item in base and current years
0i 1i
respectively.
Using these notations, we can write an expression for price relative of the ith item as
P = p 1i ´ 100 and quantity relative of the i th item as Q = q 1i ´ 100 .
i
p 0i i q 0i
Further, P will be used to denote the price index number of period ‘1’ as compared with
01
the prices of period ‘0’. Similarly, Q and V would denote the quantity and the value
01 01
index numbers respectively of period ‘1’ as compared with period ‘0’.
Self Assessment

Fill in the blanks:

5. The year from which comparisons are made is called the………………….
6. ………………………is commonly denoted by writing ‘1’ as a subscript of the variable

11.4 Price Index Numbers

Simple Average of Price Relatives

1. When arithmetic mean of price relatives is used

å P å p 1i ´ 100
p
The index number formula is given by P = i or P = 0i Omitting the
01 01
n n
å p 1 ´ 100
p 0
subscript i, the above formula can also be written as P =
01 n
2. When geometric mean of price relatives is used

The index number formula is given by

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