The base line with which prices are compared is usually the average of a series of years, the purpose of taking such an average being to over come any eccentricities of prices which might characterize a briefer period of time. This prac tice is not universal, and some well-known calcu lations have been based upon the prices of a single year. This method is justified on the ground that the prices so chosen were those of normal conditions.
In the combination of the price series into a general index of prices, the simple mean is the most frequent method employed, as illustrated in our first index calculation. This has been the subject of much criticism on the ground of the unequal importance of the objects concerned. To overcome this difficulty two sets of weighted averages have been proposed. The first was one which measured all articles by their importance in the national consumption as illustrated in the third calculation; the second measures articles by their importance in individual consumption as revealed by family budgets and typified in our second calculation. In applying national con sumption as a test, we find that calculations of such consumption are very precarious and extend to comparatively few articles. In family con sumption we can ascertain for certain groups of persons the proportions of expenditure which cover a much wider range of commodities. But the commodities covered by the family budgets are not the same as those covered by price statis tics, since the former represent the retail, and the latter the wholesale markets. In the food prod ucts this makes little difference, but in textiles, metals, lumber, and the like there is no little adjustment needed to bring the prices and the relative expenditures into relation.
Those who have done the most to establish more rational and at the same time more com plicated calculations have been the first to point out that the ultimate results differ but slightly from those obtained by the somewhat rough eat culation of a simple average.
The index number of the London Economist is based upon the wholesale prices of 47 com modities which by combination are reduced to 22. The quarterly prices for 1845 to 1850 were arranged as a basis for calculation and the rel ative prices for subsequent years upon the Janu ary prices. The total price index for 1845 to
1850 was 2200, and for later years the price in dices are also expressed as an aggregate, with out reduction to 100. As in a few eases the full number of articles was not given, this was somewhat misleading. In the following table we give the results of this calculation as published by the Economist, together with a reduction to the scale of 100: The general tendencies of price movements, the rising tendency till 1873, and the subsequent downward trend as shown in these figures are amply confirmed by other investigations. The enormous rise in the period of 1801 to 1865 was ease not only to the extravagant prices for cotton paid in this period, but also to the fact that in the twenty-two series represented in the total as many as three were for cotton. This fact, and the prominence given to indigo, and the absence of so important a staple as coal, led to numerous efforts to improve the calculation. Mr. R. H. Inglis Palgrave sought to remedy the defects by a system of weighing each article by its impor tance in the national consumption—a method al ready indicated.
Mr. Augustus Sauerbeek published in 1886 in the Journal of the Royal Statistical Society an index number which has been brought down to date in subsequent issues of that periodical, and hich is in ninny respects an improvement upon the older calculation. His annual prices are based upon averages of the monthly, and in some important commodities weekly prices, and these are compared with the average prices of 1867 to 1877. The tables embrace 45 series of quota tions: and while some commodities are repeated (in different grades), they have been chosen in such a manner that the total number of quo tations for a group of commodities such as meats, textiles, iron and steel represents approxi mately in its proportion to the whole number of quotations—forty•five—the importance of this group in the commerce of the United Kingdom. The superiority of this calculation rests, there fore, on the more trustworthy character of its material, and the breadth of choice.