ON VARIATIONS IN TIIE VALUE OF THE MONETARY STANDAUD. 209 



for all articles great and small, then, regarding our twentj-one, or it maj 

 be forty-five, articles as specimens of this series, we shall best operate on 

 them by taking their Median. 



And, even if this reasoning is not accepted, if the asymmetry of the 



price-curve should not be regarded as serious, and the central point of 



the supposed symmetrical complete curve or series be taken as the 



quassitum, still, even upon this hypothesis, the Median would have 



. special claims.' 



Another advantage — or the same otherwise viewed — on the side of the 

 Median is its insensibility to accidental alterations of 'weight.' You 

 may considerably increase or lighten the weights without causing this 

 Mean to be depressed or elated. In the Arithmetic Mean a large weight 

 happening to concur with an extreme price- variation produces a derange- 

 ment which with reference to the present objective'^ (as distinguished 

 from the 'consumption') standard may be regarded as accidental. The 

 Median is free from this fortuitous disturbance. The rationale of this 

 stability is supplied by the Calculus of Pi'obabilities, 



It appears, therefore, that our index-number, though not likely to he wide of 

 any mark which has been proposed, is not the one which is most accurately directed 

 to a particular, or rather, indeed, the most general object. It is no matter for sur- 

 prise or complaint that we should not hit full in the centre an object which has not 

 been our aim ; our index-number being mainlj' a Standard of Desiderata, measuring 

 the variation in value of the national consumption. Our primary aim, indeed, is 

 more comprehensive, not this special, but a collective, or ' compromise,' scope ; 

 not so much to hit a particular bird, but so to shoot among the closely clustered 

 covey as to bring down most game. But then we are brought back to, or nearly to, 

 the directer aim and simpler object by a consideration which has great weight in 

 practical economics, the necessity of adopting a principle — as Mill says with 

 respect to convertible currency — ' intelligible to the most untaught capacity.' 

 Now every tyro in our subject makes straight for the Consumption Standard ; but 

 the more delicate distinctions of the Producers' Standard and the typical or quasi- 

 objective index-number evade popular perception. 



In view of this practical exigency it may well be that the Committee's index- 

 number is the one best adapted to purposes in general — the principal standard as 

 ■defined in the First Report. What is here contended is that, with respect to a 

 certain purpose other than the consumers' interest, the Committee's index-number 

 is on the one hand likely to be a very good measure, and on the other hand not 

 the very best possible. 



B. 



We have now to compare index-numbers differing as to the prices 

 operated on as well as the methods of operation. One important case 

 is where the prices of the principal articles are the same for the com- 

 pared index-numbers, the data differing only as to ii small part of the 

 total value. For example, of the total value covered by Mr. Sauerbeck's 

 index-number about -^^ is common to the Committee's scheme. For 

 Mr. Sauerbeck's weights (or ' nominal values ') of the twenty-one 

 articles common to both calculations make up (for the year 1885) 659, 

 while the sum for all the items treated by him is 617. 



' The problem would then be analogous to the reduction of symmetrical observa- 

 tions relating to a physical quantity. On account of the ' discordance ' of the price- 

 observations, their very different liability to fluctuation, the writer would recommend 

 the use of the Median on the grounds which he has stated in the paper on ' Discordant 

 Observations,' Phil. Mag., April 1886. 



^ See ' Memorandum,' Rej)ort of Brit. Assoc, 1887, and also Journal of the Statis- 

 tical Society, June 1888. 



1888. P 



