# what is a index number?limitation of index number?

An index number is a statistical device used to measure changes in the related variables. In other words, index numbers helps in assessing the changes in the values of the variables over time in comparison to a particular year (base year).

Consider the following example. Here, prices of five commodities is given for base year (P0) and current year (P1)

 Commodity P Q R S T Prices in base year (P0) 12 15 18 20 22 ΣP0 = 87 Prices in current year (P1) 14 17 17 21 25 ΣP0 = 94

Limitations of index numbers

The following are some of the limitations of index numbers

• Based on samples, and hence cannot be generalised thereby, not revealing a holistic view.
• Acts merely as an approximation.
• Fails to reveal the qualitative aspect of the variable under study.
• More probable to give misleading and erroneous results, if wrong base year is selected.
• It is objective specific. Index number constructed for one study cannot be used for another study.

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What are index numbers?
Index numbers are designed to measure the magnitude of economic changes over time. Because they work in a similar way to percentages they make such changes easier to compare. Briefly, this works in the following way.
Suppose that a cup of coffee in a particular café cost 75p in 1995. In 2002, an identical cup of coffee cost 99p. How has the price changed between 1995 and 2002?
The particular time period of 1995 which we've chosen to compare against, is called the base period.
The variable for that period, in this case the 75p, is then given a value of 100, corresponding to 100%.
The index can then be calculated for the later period of 2002 as a proportionate change as follows:

The index number shows us that there has been a price increase of 32% since the base period. An index number for a single price change like this is called a price relative.

Rule for finding the price relative
If we let po be the price in the base period and let pn be the price in the later period, then the price relative for the price change between these periods is given by (pn/po) x 100.

Limitations of Index Numbers

• They are simply rough indications of the relative changes.
• The choice of representative commodities may lead to fallacious conclusions as they are based on samples.
• There may be errors in the choice of base periods or weights etc.
• Comparisons of changes in variables over long periods are not reliable.
• They may be useful for one purpose but not for other.
• They are specialized types of averages and hence are subject to all those limitations with which an average suffers from.
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