402 Rkport S.A.A. Advancement of Science. 



and iiiediuin tint. He is (says Bowley) a more satisfactory model than 

 the newspapers' "average," for in regarding him we see the type from 

 whicli all other men may be supposed to have deviated — the creature 

 that would have been produced if all disturbing causes were removed. 

 TJiat any actual person should answer exactly to all these standards is, 

 of course, in tlie highest degree improbable. 



Objection's have been raised from time to time against Quetelet's 

 methods of determining his "mean" or ."average" man. All the 

 same, his work is of lasting merit. Professor Edgworth in a paper 

 read before the British Association in 1893 pointed out tliat, if it 

 were required to construct a budget of a typical workman's family 

 upon several articles of food, rent, &c., the case would be analogous 

 to that ti'eated by Quetelet when he sought to construct an average 

 man b}' measuring the limbs or organs of a great number of men and 

 taking the mean of the measurements relating to each part as the type 

 of that part. It has been objected, however, that the parts thus deter- 

 mined might not fit each other. It has been said that the procedure 

 of Quetelet is like that of a person who, having taken several observa- 

 tions of each angle of a triangle, should put the mean of each set of 

 observations for the value of the corresponding angle. The three angles 

 thus determined might not form two right angles 1 Similarly, the organs 

 determined by Quetelet's method uiight not fulfil the conditions of joint 

 existence. The "mean" or "average" man might be a monster, not a 

 model ! Edgworth successfully defends Quetelet, and shows that this 

 criticism is not well founded. 



Alth<:)Ugh Quetelet's (hscovery of tlie binomial law was made more 

 than sixty years ago, very little fresh development seems to have been 

 made in this long interval. Bowley, in a paper read before the British 

 Association in 1 906, regrets the lack of interest on this subject. He 

 points out that the use of mathematical reasoning in statistics is very 

 imperfectly undei'stood, partly because the passage from numbers to 

 syml)ols and back to numbers suggests an air of myster}^ or even of 

 prestigiation, to the unmathematical mind, partly because the method, 

 although fully sixty years old [Quetelet's letters were published in 

 184G], lias only recently been de\eloped, and the methods and limi- 

 tations of its use are still a matter of analysis and discussion among 

 its advocates. There are those who hold that verbal or numerical 

 reasoning, unassisted by symbols, is suHicient for the elucidation of all 

 truth. 



Bowley, I tliink, takes rather too gloomy a view as to the progress 

 of mathematical methods in statistics. Even the newspapers aT-e now 

 calling for sometliing more than a mere collection of figures. 



On this question, the following extracts from an article in the 

 S(Uard(iij lievieir of 15th Februar3\ 1908, will be of interest. The 

 article is headed, "Idle Figures about Working Folk. A Board of 

 Trade Folly." It proceeds: "The report of the Board of Trade on 

 working-class rents, housing and retail prices and standard I'ates of 

 wages is about as inconclusive and unsatisfactory a piece of work as 

 even the Boaid has evei- isssned. ]t is a huiie volume of over six 



