Page 214 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes For a proper understanding of the term index number, the following points are worth considering:
(1) Index numbers are specialized averages : As explained in unit 4 central value, an average is a
single figure representing a group of figures. However, to obtain an average, items must be
comparable; for example, the average weight of men, women and children of a certain locality
has no meaning at all. Furthermore, the unit of measurement must be the same for all the items.
Thus an average of the weight expressed in kg., lb., etc., has no meaning. However, this is not so
with index numbers. Index numbers are used for purposes of comparison in situations where
two or more series are expressed in different units or the series are composed of different types
of items. For example, while constructing a consumer price index the various items are divided
into broad heads, namely (i) Food, (ii) Clothing, (iii) Fuel and Lighting, (iv) House Rent, and (v)
Miscellaneous. These items are expressed in different units : thus under the head ‘food’ wheat
and rice may be quoted per quintal, ghee per kg., etc.
Similarly, cloth may be measured in terms of metres or yards. An average of all these items
expressed in different units is obtained by using the technique of index numbers.
(2) Index numbers measure the change in the level of a phenomenon : Since index numbers are
essentially averages they describe in one simple figure the increase or decrease in the level of a
phenomenon under study. Thus if the consumer price index of working class for Delhi has
gone up to 125 in 2005 compared to 100 in 2004 it means that there is a net increase of 25% in the
prices of commodities included in the index. Similarly, if the index of industrial production is
108 in 2005 compared to 100 in 2004 it means that there is a net increase in industrial production
to the extent of 8%. It should be carefully noted that even where an index is showing a net
increase, it may include some items which have actually decreased in value and others which
have remained constant.
(3) Index numbers measure the effect of change over a period of time : Index numbers are most
widely used for measuring changes over a period of time. Thus we can find out the net change
in agricultural prices from the beginning of first plan period to the Ninth plan period, i.e., 1997-
2002. Similarly, we can compare the agricultural production, industrial production, imports,
exports, wages, etc., at two different times. However, it should be noted the index numbers not
only measure changes over a period of time but also compare economic conditions of different
locations, different industries, different cities or different countries. But since the basic problems
are essentially the same and since most of the important index numbers published by the
Government and private research organisations refer to data collected at different times, we
shall consider in this chapter index numbers measuring changes relative to time only. However,
methods described can be applied to other cases also.

“Index numbers are devices for measuring differences in the magnitude of a group
of related variables.”

Meaning and Definition

Index numbers are the specialised averages designed to measure the changes in a group of related
variables over a period of time. Some important definitions of index number are given below. They
would help in understanding about what index numbers are :
(1) According to Spiegel, “An index number is a statistical measure designed to show changes in a
variable or a group of related variables with respect to time, geographic location or other
characteristics such as income, profession etc.”
(2) As per Morris Homburg, “In its simplest form, an index number is nothing more than a relative
number or a ‘relative’ which expresses the relationship between two figures, where one of the
figures is used as base.”
(3) A. M. Tuttle suggests, “Index number is a single ratio (usually in percentages) which measures the
combined (i.e., averaged) change of several variables between two different times, places or situations.”

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