INDEX NUMBERS. The phrase index number is some times applied to any series in which a chosen term is written as and the other terms expressed as percentages of it. The earlier and more general use is, however, consonant with the following definitions : "An index number [is] a number adapted by its varia tions to indicate the increase or decrease of a magnitude not sus ceptible of accurate measurement" (Edgeworth, Economic Jour nal, p. 379) ; "index numbers are used to measure the change in some quantity which we cannot observe directly, which we know to have a definite influence on many other quantities which we can so observe, tending to increase all or diminish all, while this influence is concealed by the action of many causes affecting the separate quantities in different ways" (Bowley, Elements of Statistics, 1920, p. 196). Thus index numbers are applied to the measurement of the general movement of prices, cost of living, wages, production, consumption, employment, etc.
The data from which index numbers are formed consist of records of particular quantities at two or more dates or places and information about the relative importance of these quantities in a general measurement. In constructing an index number to measure the movement of any defined magnitude it is necessary to decide on the choice of the separate quantities, on their rela tive importance, on the period or place to be taken as base, and on the formula of compilation. Thus, in the Statist index number the objective is the measurement of the change of wholesale prices in the United Kingdom ; 45 commodities are selected and regarded as of equal importance, the period 1867-77 is taken as base, the average price in that period of each commodity is equated to the terms in each series of prices are expressed as percentages of that average ("price-relatives"), and the simple average of the 45 relatives in any year forms the index number for that year.
A distinction is drawn, but not by all writers, between two classes of index numbers: (a) where, as in the definitions quoted above, the object is to measure the movements of a magnitude without specific reference to any pre-determined application, e.g., the purchasing power of money in general ("indice monetaire") as conceived by Jevons, The Variation of Prices and the Value of Currency since 1782 (1865); (b) where the measurement is to be applied to a defined group, e.g., the changes in the cost of a quantitative standard, such as is used in a cost of living index ("indice budgetaire"). Many index numbers, however, are inter mediate between these classes, and much of the analysis of the form and content of the numbers is appropriate to both. Thus, in all cases of price measurement, only those commodities can be included which are measurable in a defined and unchanged unit, and for which the price can be ascertained, and (unless the geo metric mean is used) a base period in which each price is equated to ioo must always be selected.