Index numbers are a means of expressing each value in a series as a proportion of the value in one year, often the value of the first year in the series, to see what proportionate changes are taking place. Index numbers are thus an artificial unit of analysis, created by effectively 'scaling' a set of figures by one particular figure.

Such a procedure is particularly valuable when the units of the time series are particularly awkward to handle; wage rates, for example, are often given in shillings and pence, and changes in them can be much more easily appreciated if they are given in the form of an index number.

Let's start with a very simple example, the value of exports for four years taken from Floud's Introduction to quantitative methods for historians (1979, p. 123). From this it is easy to show how index numbers are calculated.
 

The calculation for base 1820=100 is shown above; how would we calculate base 1850=100 to produce the results detailed?

In many series which have a rising trend, choosing an early year as a base will give an impression that the series is growing rapidly, while choosing a later year will seem to reduce the growth. There is in fact no difference in the proportionate change. In the above example the percentage change over 1820-50 is identical irrespective of the base years, either 196.2/100 or 100/50.9 (at approximately 96%). Equally, in a series that shows considerable fluctuations, the series of index numbers will give a different impression depending on whether the base year chosen is a year of considerable upward or downward fluctuation from the trend.

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(c)R. Middleton 1997. Last modified 29 June 1998.