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Unit 15 : Index Number–Introduction and Use of Index Numbers and their Types

which base year to be selected, what items should be selected, which formula should be chosen Notes
and so on. If clearity of purpose is assured most of these problems can be solved. Regarding
obtaining proper quotations, efforts should be made to choose reliable sources, and items chosen
should be standardised and graded, so that quotations are easily and accurately obtained.
15.3 Types of Index Numbers

Price Relatives

One of the simplest types of index numbers is a price relative. It is the ratio of the price of a single
commodity in a given period or point of time to its price in another period or point of time, called the
reference period or base period. If prices for a period, instead of a point of time, are considered, then
suitable price average for the period is taken and these prices are expressed in the same units.
If p and p denote the price of a commodity during the base period or reference period (0) and the
0 n
given period (n) then the price relative of the period n with respect to (w.r.t) the base period 0 is
p n
defined by price relative in percentage (of period n w.r.t. period 0) = p 0 × 100 ... (1)

and is denoted by p .
0/n
For example, if the retail price of fine quality of rice in the year 1980 was Rs. 3.75 and that for the year
1983 was Rs. 4.50 then

Rs. 4.50
p 1980 |1983 = Rs. 3.75 ×100 = 120%

For example, the exchange rate of a U.S. dollar was Rs. 10.00 in July 1984 (period J) and was Rs. 12.50
in December 1984 (period D) then the price relative of a dollar in December w.r.t. that in July is given
by
Rs.12.50
=
p J|D Rs.10.00 × 100 = 125%

Quantity Relatives
Another simple type of index numbers is a quantity relative, when we are interested in changes in
quantum or volumes of a commodity such as quantities of production or sale or consumption. Here
the commodity is used in a more general sense. It may mean the volume of goods (in tonnes) carried
by roadways, the number of passenger miles travelled, or the volume of export to or import from a
country. In such cases we consider of quantity or volume relatives. If quantities or volumes are for a
period instead of a point of time, a suitable average is to be taken and the quantities or volumes are
to be expressed in the same units. If q and q denote the quantity or volume produced, consumed or
0 n
transacted during the base period (0) and the given period (n) then quantity relative of the period n
w.r.t. the base period 0 is defined by quantity relative in percentage (of period n w.r.t. period 0) =
q n × 100
q 0 ... (2)
and is denoted by q .
0|n
Value Relatives

A value relative is another type of simple index number, usable when we wish to compare changes
in the money value of the transaction, consumption or sale in two different periods or points of time.
Multiplication of the quantity q by the price p of the commodity produced, transacted or sold gives
the total money value pq of the production, transaction or sale. If instead of point of time, period of
time is considered, a suitable average is to be taken and is to be expressed in the same units.

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