De invloed van de keuze der gewichten op de hoogte van een gewogen indexcijfer

The influence of the choice of the weights on the value of an indexnumber. Price and quantity indexnumbers are weighted averages of groups of price and quantity ratios and they are convenient instruments to indicate the general tendency of such groups, especially if the number of basic ratios is considerable. The frequent use of indexnumbers is due to the fact that they can often be applied to problems for which, strictly speaking, an indexnumber had to be used derived from the same group of ratios but based on a different set of weights. Two typical examples of such problems are given. The use of a set of weights differing from the appropriate one is only justified, however, when the indexnumber is rather insensitive to changes in the set of weights. A simple formula is derived showing that the relative change of an index‐number due to a change in the set of weights is equal to the product of the (weighted) coefficient of variation of the basic ratios, the (weighted) standard deviation of the relative changes of the weights and the (weighted) coefficient of correlation of the ratios and of the relative changes. The system of weights used in the calculation of these three factors is the same and is equal to the set of true weights belonging to the problem under consideration. The practical use of the formula is demonstrated at the problem of index‐numbers of costs frequently encountered in the practice of cost accounting.