ox YABIATIONS IN THE VALUE OF THE MONETARY STANDAHD. 159 



A27 3031323334 3637 40414243 46 47 4849505152 59 64 



29 31323334 36 3839 41 43444546 4950 5253 5657 59 62 



C 38 404142 44 4647 49 505152 54 5758 61 



4041 44 46 50 5758 



40 50 57 58 



It appears, then, that, though our end is tho greatest ordinate of the 

 complete series, the best mean — if we may be excused a pun which it is 

 not easy to avoid — is not necessarily the greatest ordinate of the sample 

 group. The position of greatest frequency is an object, like happiness, 

 best reached by not aiming at it too directly. 



The indirect and ancillary average need not be the one which we 

 have taken for the sake of illustration in the last paragraph. In fact, in 

 the case there instanced the arithmetic mean would be the preferable 

 method. But in the case of prices there is reason to believe that tho 

 median is peculiarly appropriate. The nature and varieties of this mean 

 have been fully discussed by the present writer both in his former 

 Memorandum on the same subject as the present one, and also in the 

 Memorandum of 1888 On the Accuracy of Index-numbers. 



However, it may not be out of place here to give an additional 

 example taken from the statistics of exports. In the annexed table each 

 figure in the first column (on tho left hand) expresses a proportion 

 between the price of an article in 1887 and the price of the same article 

 in 1883. Thus, the price of gunpowder per lb. being in 1887 6"46d. and 

 in 1883 5'83(Z., we have the proportion, or comparative price, 111=10Q 

 X6-46-HO-83. 



Opposite each comparative price are written in the second column or 

 space the values of the corresponding articles for 1887, the proportionate 

 values or actual values divided by a certain figure which is the same for 

 all the entries, viz., 240,000. For instance, the value of gunpowder is 1, 

 being, in round numbers, its actual value 260,000 divided by 240,000. 

 With the reason for adopting this divisor we are not here concerned. 

 Any other basis would serve our purpose as well. It often happens that 

 the same proportion of price is enjoyed by two articles. Thus the com- 

 parative price 127 appertains both to arms (fire) and to silk, of which 

 articles the proportionate values are respectively 1 and 6. Accordino-ly 

 against the entry 127 are Avritten (it does not matter in what order) the 

 figures 1 and G. Both the prices and the proportions of value are taken 

 from the table given by !Mr. Bourne in the paper on Index-numbers con- 

 tributed by him to the Report of the British Association for 1888. 



Well, then, the simple or unweighted median is thus found. There 

 being in all G4 proportions (some of them coincident), we are to select 

 that one which has as many returns above it as below ; in short, a point 

 between the thirty-second and thirty-third in the order of magnitude. 

 This is easily effected by counting up the numbers of the * proportionate 

 values ' in the right-hand space. Tho thirty-second and thirty-third, 



