218 REPORT— 1888. 



weight according to Mr. Sauerbeck for wheat; in a curtailed index- 

 number covering only those articles common to him and the Committee. 

 By parity -g'^.j x lUO, or six nearly, is the weight for the same article 

 according to the Committee. In the sixth column the differences — the 

 absolute differences without regard to sign — between the respective 

 weights are given. To appreciate the importance of this difference of 

 weight, we must consider it in relation to the absolute (mean) weight. 



mi Mean difference of weight ■ .-, n ,• , t,- t j i taa j.i 



Thus ■ — IS tbe traction (or, multiplied by 100, the 



Mean weight 



percentage) which most, or at least very, properly measures the dis- 

 crepancy between the two systems. Now the Mean weight for each of 

 the two compared systems is ^^x . Therefore we have for the required 



Sum of differences .inn • ^ Sum of differences / 

 measure — — Vy', or simply — — (or, ex- 



pressed as a percentage, the sum of differences). Thus in the case before 

 us the average deviation between the compared weights is 46'5, or 47 per 

 cent, (nearly). This figure is useful as enabling us (taking into account 

 the number of common items) to predict the extent of discrepancy which 

 is likely to exist between the results of the two methods of treating the 

 common data. 



The second table presents a similar comparison between the Com- 

 mittee's and Mr. Palgrave's index-number (' Third Heport of the Com- 

 mittee on Depression of Trade,' Appendix B). It has not been 

 thought necessary to record the actual weights. Those employed in the 

 computation of the ' relative ' weights according to Mr. Palgrave were the 

 figures of compa7-ative importance given by him for the year 1885, which 

 differ very little from the corresponding entries in previous years. The 

 coefficient of discrepancy between the two systems being much the same 

 as in the former comparison, we may expect much the same difference 

 between the results ; or rather one somewhat larger, since the number of 

 common items (sixteen) is here somewhat smaller (than twenty-one). 



The remaining index-numbers do not equally admit of being laid 

 alongside that of the Committee for the purpose of comparison. 

 They are as it were in a different plane, adopting a different formula 

 (as well as different constants) from the Committee. In these 

 schemes, unlike the Committee's, each comparative price is not affected 

 with a factor or weight corresponding to its importance. Prima facie 

 every price- variation counts for one ; but the principle of weight is to 

 some extent asserted by introducing as independent items several species 

 belonging to one genus. Thus in Mr. Sauerbeck's umveighted index- 

 number, our Table 3, there figure tivo species of wheat and also one of 

 flour ; in effect assigning a weight of three to wheat. There is indeed 

 something arbitrary in such interpretation. For in comparing this sort 

 of index-numbers with the Committee's it is hardly possible — as in the case 

 of the explicitly weighted index-numbers — to suppose the prices (for the 

 common articles) to be the same in the two compared calculations. For 

 example, our price of wheat is taken from the ' Gazette ' ; theirs may be 

 a Mean of that price and the price of flour. Accordingly the estimate of 

 the difference to be expected (proportioned to the total of the last column) 

 is apt to be less accurate, to be under the mark, in these cases. A further 

 inaccuracy affects this estimate in the case of Jevons' index-number, our 

 Table 5, namely, that he adopted the Geometrical method of combining 

 price- variations. In fact, our estimates apply only to the Arithmetic com- 



