28 American Statistical Association. 



thousand. Eacli group, tlierefore, will be characterized by a 

 physical development definitely determined by the means of 

 height, weight, and other physical dimensions. These means 

 taken together form the typns or norm of the group. The 

 individual deviations from this norm follow the theory of 

 probability, and the degree of abnormality presented by any 

 individual deviation can be expressed in the terms of tliis 

 theory. An example will illnstrate this: A boy a? shows a 

 deviation in height oi -\-l^ b d from the mean height of his 

 age; he falls therefore in group III. The boys in this group 

 possess a mean weight of M^ kilog., with a probable deviation 

 of -\-d^^ that is, boys from d to 2 d taller than the norm of 

 their age should weigh J/^-j-cZ^ kilog. In like manner they 

 should possess a girth of chest of M'^-\-d'^ centimetres, and 

 a span of arms of 31^ -\- d^ cm., and so on. If the weight, 

 etc. of the boy x coincide with the means of his group (group 

 III) his physique is normal, the accuracy of this conclusion 

 being proportionate to the number of different measurements 

 on which it is based. If the boy x deviate more than ± d 

 from the mean in one or more dimensions his development is 

 abnormal, and the degree of abnormalit}^ is measured by the 

 amount of his deviation. 



The necessity of choosing some one dimension as a basis 

 of such a system of measurement is self-evident. There are 

 good reasons, partly theoretical and partly practical, why 

 height rather than weight should be takeii as a basis. Height 

 is more stable, less liable to irrelevant fluctuations than 

 weight. An excess in weight can be reduced; a child whose 

 weight is out of proportion to its height may be brought into 

 proportion b}^ suitable diet and exercise; but height once 

 attained cannot be reduced, nor can the growth in height be 

 easily influenced. Practically, therefore, the pli3^sical trainer 

 must be content to bring the weight, girth of chest, strength 

 of squeeze, and other physical dimensions up to the mean 

 development which corresponds to the height of the child. 

 Experience has abundantly shown that the relation of weight 



