1170 



VITAL STATISTICS. 



words, to do for this important, branch of 

 statistics what has been done elsewhere for 

 the statistical or numerical method.* Having 

 already insisted on the precautions to be ob- 

 served in the use of numbers as a scientific 

 instrument, it remains to determine the pre- 

 cise value of those measures of the duration 

 of life which are in common use for scientific 

 and practical purposes. 



On a superficial view of the subject, it 

 might seem sufficient, in order to determine 

 the mean age attained by a given class of 

 persons exposed to a given class of influence^, 

 to collect the ages, at death, of a certain 

 number of persons belonging to that class, to 

 add those ages together, and to divide the sum 

 by the number of persons. But it must be 

 evident, on further consideration, that an 

 average so obtained may furnish a very im- 

 perfect measure of the longevity of the class, 

 and of the force of the influences brought to 

 bear upon the individuals of whom it is com- 

 posed. 



In order to build up a science of Vita! 

 Statistics 'mother words, in order to deter- 

 mine the true influence of external agents on 

 the duration of human life, we must make 

 use of such materials as happen to be ready 

 to our hands. These materials do not always 

 present themselves in the same shape, nor do 

 they all possess the same value. Sometimes 

 they are simple averages ; at other times they 

 are complex calculations based upon the same, 

 or similar facts, but moulded into new forms 

 by means of certain necessary corrections. A 

 few preliminary observations on these mate- 

 rials will be found to answer several useful 

 purposes. They will serve, at one and the 

 same time, as a test of the value of the prin- 

 ciples sought to be established, and as a 

 check to the tendency with which the statist 

 is often reproached to exaggerate the value of 

 inferences drawn from numerical data. 



Several methods are in use for measuring 

 the duration of human life. Of these, the 

 best known and most commonly employed 

 are the following: 



1. The mean age at death ; 2. The rate of 

 mortality; 3. The expectation oflife ; 4. The 

 mean duration of lite ; and 5. The probable 

 duration of life. Other terms, such as the 

 specific intensity of life, and other methods, 

 such as the age$ of the living, are occasionally 

 employed. 



I. The mean age at death. The mean, or 

 average age at death, is the sum of the ages 

 at death, divided by the number of deaths. 

 Thus, if five persons die at the respective ages 

 of 20, 30, 40, 50, and 60, their mean, or 



. t , . 20 + 30 + 40 + 50 + 60, 

 average age at death is - 



o 



or 40 years ; and if a second group of five 

 persons die at the respective ages of 20, 

 35, 50, 65, and 80, their mean age at death is 

 20+35 + 50 + 65 + 80 , Qr 3Q ^^ N<w> if 



o 



these two groups of five persons were each 

 exposed during their lives to a peculiar set of 



* See STATISTICS, MEDIC AT,, p. 801. 



influences, the mean age which they respec- 

 tively attained would be a measure of the 

 force of those influences. But such a mea- 

 sure would be open to the serious objection 

 that the number of facts from which the 

 averages are calculated is insufficient. Let 

 us, however, suppose this objection to be set 

 aside by increasing the number of deaths in 

 each case to several hundreds or thousands, 

 so as to embrace either the entire number of 

 deaths of the classes submitted to comparison, 

 or such a considerable proportion of deaths 

 taken without selection as would give satis- 

 factory results in accordance with the strictest 

 requirements of the numerical method, the 

 question still presents itself, Is the mean age 

 at death a safe measure and standard of com- 

 parison ? The answer to this question must 

 be in the negative. The mean age at death is 

 not always a safe and sound standard. Its 

 employment would often lead to very erro- 

 neous inferences. It will therefore be neces- 

 sary to discriminate between those cases in 

 which it may be employed with safety, and 

 those in which its use would lead to fallacious 

 results. 



The mean age at death can be employed 

 with safety as a true test or measure only in 

 those cases in which the calculation purport- 

 ing to embrace an entire class of persons, 

 every member of that class is included, or in 

 which the calculations embracing only a sec- 

 tion of an entire class, the class in question is 

 retained in a state of perfect uniformity during 

 the whole time comprised in the calculation. 

 According to the first supposition, we take a 

 given number (say 100,000) of children born 

 in a given year, and trace them through life 

 till they are all dead, summing up their ages 

 at death, and dividing by the number of deaths. 

 According to the second supposition, we ex- 

 tract from some register of deaths the ages of 

 all who die during some term of years, having 

 ascertained, by referring to the CLIISUS, that 

 the population has continued stationary (that 

 is to say, constantly gaining as many by fresh 

 births as it loses by death), during the time 

 over which the calculations extend. The 

 same reasoning will be found to apply to the 

 mean age at death, taken as a measure of the 

 true duration of life of the members of any 

 handicraft, trade, or profession. It can only 

 be a true measure so long as the blanks 

 caused by death are filled by new recruits, 

 entering at the same age as the age of entrance 

 of the deceased. In all other cases but those 

 now specified, the mean age at death is a 

 more or less fallacious measure of the true 

 duration of life. 



As the mean age at death has been lately 

 revived as a measure of the duration of human 

 life, and a test of the sanitary condition of 

 the population, though its fallaciousness was 

 long since recognised and pointed out by the 

 early constructors of life-tables, it may be 

 well to devote some space to a statement of 

 the cases in which the proposed test is most 

 open to objection. 



a. The mean age at death has been employed 

 as a test of the sanitary condition of a nation, 



