The Growtli of St. Louis Children. 69 



I purpose ill this paper to give a brief account of some of 

 the results of these studies. 



It is a matter of much interest to determine whetlier meas- 

 urements made for the most part by teacliers in the public 

 schools are sufficiently accurate to furnish reliable physical 

 standards. The statistician answers this question by compar- 

 ing the observed distribution of the heights or weights, etc., 

 at any age with the distribution of an equal number of obser- 

 vations according to the theory of probabilities. A glance 

 at the theoretical and the observed distribution of the heights 

 of 2192 girls, aged 8 (Table No. 7 in The Gro^vth of St. Louis 

 Children), shows a satisfactory agreement between them. 

 Tliis indicates that the number of measurements is so large 

 that deviations to one side of the true height are fairly well 

 compensated by deviations to the other side. In such a case 

 the median value of the series is typical of the series. Thus, 

 in this investigation measurements collected by comparatively 

 unskilled observers were found to satisfy the requirements 

 of theory. 



The objection sometimes made that the errors of observa- 

 tion materially affect the truth of the values obtained is of 

 little weight, partly because such errors are " accidental *' 

 and compensate each other, and partly because a deviation 

 from the middle value due to an uncompensated error in 

 measurement forms, as a rule, an inconsiderable part of that 

 greater deviation which expresses the physiological difference 

 between the individual and the type of his age and class. 

 ''Accidental " errors of observation need not give concern in 

 measurements of great numbers of school children. Nor need 

 there be much fear of constant errors of observation, pro- 

 vided the collection of material is made by many persons, and 

 with a good number of each sort of measuring instrument. 



The degree of deviation of individual measurements from 

 the median value of an anthropometrical series is measured 

 by the Probable Deviation, that value which, in the words of 

 Lexis, is as often exceeded as attained. Hence, if Quetelet's 



