808 



STATISTICS. 



training which is essential to the appreciation 

 of mathematical rules, it is desirable to show, 

 by an appeal to the results of actual observ- 

 ation, the increasing value of increasing col- 

 lections of facts, as well as the rate of that 

 increase. For this purpose, it is proposed to 

 make use of some observations collected by 

 the writer of this article. Having had occa- 

 sion, a few years since, to bring together, from 

 the pages of the Peerage and Baronetage, the 

 ages at death of the male members of the En- 

 glish aristocracy, dying 21 years and upwards, 

 to the number of several hundreds, it ap- 

 peared to be a favourable opportunity of test- 

 ing the relative values of large and small 

 numbers of facts, as well as of obtaining a 

 rude approximation to a rule or measure of 

 value. The ages at death, relating, as they do, 

 to members of the same class in society, and 

 taken without selection from the successive 

 obituaries of noble families, constitute a col- 

 lection of strictly comparable facts, well suited 

 to the purpose in view. The following table, 

 \vhich embodies the results of these facts in 

 their bearing on the question before us, has 

 been formed in the following manner : The 

 several facts were first arranged in groups of 

 25 each; two successive groups of 25 were 

 then formed into groups of 50 ; the groups of 

 50, in like manner, into groups of 100, and so 

 on, till the last totals in the table were ob- 

 tained. The greatest and least averages ob- 

 tained from each group of facts were then 

 selected, and, with the range, or difference be- 

 tween them, thrown into a tabular form. 



i if we assume the true average duration 

 of life among the members of the Peerage and 

 Baronetage, who have attained their 21st year 

 to extend to 60 years (being the mean of 

 1600 observations), and, for the sake of 

 bimplicity, substitute for the decimals in the 

 table the whole numbers nearest to them in 

 magnitude, it will follow that, in making use 

 of the several groups of observations specified 



in the first column of the annexed table, we 

 may have the errors in excess or in defect 

 which are enumerated in the second column. 

 These figures, then, represent the extreme 

 error which could have been committed, in 

 this particular case, by relying on 25, 50, 100, 

 200, 400, and 800 facts respectively. But it 

 must be borne in mind, that this collection of 

 facts is one which, from the very nature of 

 the case, is likely to present a minimum of 

 divergence between the averages deduced 

 from the same number of facts ; for the several 

 obituaries, from which the ages at death are 

 taken, register the deaths of one and the same 

 class, inhabitants of the same country, and 

 split into family groups bearing a close re- 

 semblance to each other. If, instead of a 

 single class, exposed to similar influences, and 

 not admitting of subdivision into smaller 

 classes, we were to take the members of that 

 large section of the community which is ge- 

 nerally known as the upper and middle class, 

 with their numerous subdivisions of employ- 

 ment, and class them by fifties and hundreds, 

 we should encounter a much more consider- 

 able divergence. The results of such a com- 

 parison for the class in question are embodied 

 in the following table. 



If, as in the former case, we take 66 years 

 to be the true average age attained by the 

 entire middle class, reckoning from 21 years 

 of age, and reduce the range in each case to 

 the nearest whole number, we shall have the 

 following divergences. 



In this instance, therefore, though we begin 

 with 50 in place of 25 facts, we obtain a 

 possible error in excess or defect of 14 years 

 in place of 9| years. It must be obvious, 

 then, that the errors to which averages de- 

 duced from any given number of facts are 

 liable, will vary with the nature of those facts ; 

 and that the extent of possible error will bear 



