212 



REPORT — 1888. 



the formula just given has been used. But it has been thought allowable to 

 deduce x not from the Mean square of error (as theoretically best), but from the 

 Mean error given in the second column of the table, putting x = </"■ x Mean error. 

 The calculations of x' and x" have been similarly rough. 



Of course, as the number of items common to two compared index- 

 numbers is diminished the chances of their dissUience are increased. 

 The art of conjecturing can in such a case throw only a very feeble light — 

 offered by the third formula above — on the relation between two such 

 index-numbers. For instance, it could hardly have been predicted that 

 the Simple Arithmetic Mean for Mr. Sauerbeck's forty-five articles should 

 differ so little as '5 from the same Mean for twenty-one articles, as 

 proved to be the case for the year 1873. It is even more surprising that 

 if for 1885 we complete our index-number, taking account of the six 

 items belonging to our scheme not included by Mr. Sauerbeck, there is 

 a marked rise in the index-number owing to all these six returns being 

 above the average. The annexed little table is formed by comparing the 

 prices in 1885 with the average for 1866-77 as given in the Statistical 

 Abstract : — 



If we add the outcome of this table to that of the first table repre- 

 senting the other twenty-one articles, we have 1665 + 5952= 7617 ; which, 

 divided by 100, gives the new index-nnmber 76. 



Of course in applying the doctrine of Chances to this problem we 

 must abstract all animus. If you pick out the large variations of price 

 and the large weights you will doubtless succeed, like Mr. Forsell, in 

 producing discrepancies — though even his success in that attempt seems 

 less than might have been expected. 



In concluding this comparison of results the writer may say, in the 

 phrase of Jevons, that he has taken more than reasonable pains to secure 

 arithmetical accuracy. No doubt mistakes will have come. But, as the 

 calculations have been performed without any conscious bias, any animus 

 mensv.randi, it may be hoped that the errors will neutralise each other, 

 and that the general impression left by the work is correct. 



' Fish imported. ' Spirits other than rum and brandy. 



