^06 



REPORT 1888. 



recorded by him) may be omitted from this little group. The Mean of 

 the group so constituted is to be placed along with the price- variations 

 for the remaining eighteen articles common to us and Mr. Sauerbeck, and 

 the Geometric Mean of all the nineteen is to be taken. It proves to be 

 €9, presenting the comparison herewith exhibited.' 



The Committee's Weisrhted Mean of 21 articles 



The slightly adjusted Geometrical Mean of the same 



70-6 



69 



The slightness of this divergence is conformable to theory. For it has been 

 shown that the Weighted Mean (of twenty-one articles) is not likely to differ very 

 much from the Simple Arithmetic Mean of the same. And it may be shown that 

 the Arithmetic Mean is not likely to differ very much from the Geometric when the 

 number of price-observations is large, and if they are not very unequal. This pro- 

 position may be illustrated by the following figures, the first row of which is 

 obtained by taking the Arithmetic Mean of the thirty-nine price-percentages given 

 by Jevons in his paper on a 'Serious Fall,' &c. (^Currency and Finance, p. 44.) 

 The second row consists of the Geometric Means, as given by him at p. 46, for the 

 same figui-es. The superior magnitude of the Arithmetic Mean will be noticed. 

 This circumstance (which Jevons thought an advantage on the side of his pro- 

 cedure) could not be predicated of a Weighted Arithmetic Mean (such as our index- 

 number), as compared with the Geometric : — 



IV. We come now to the Median, which has been recommended by 

 the present writer as the formula for the most objective sort of Mean be- 

 tween prices, not directed to any special purpose, such as the wants of the 

 consumer or the difficulties of the producer, but more impersonal and 

 absolute. 



Of the twenty-one price- variations for 1855 given in column 1 of 

 table 1, we have to take that which is the eleventh in the order of magni- 

 tude. To ascertain this we need not arrange all the figures in order. 

 Having an inkling that the Mean is between 70 and 80, we shall find it 

 sufficient to note the number of returns which lie outside those limits, and 

 to write down in the order of magnitude only the returns which lie 

 between 70 and 80. Thus, running our eye down the column of figures, we 

 make a dot on the right for every return which is greater than 80, on 

 the left for every one less than 70 ; and write down in the central com- 

 partment the figures which lie between 70 and 80 inclusive. Whence it 



' If we lump together Barlet/ and Oatt into one group, Sugar and Tea into 

 another, and again Copper and Lead, the Geometric Mean of the sixteen returns 

 thus presented is 70' 2. 



