22 American Statistical Association. 



gymnasia is fault}-. If the teacher of the gymnasium is 

 given a pupil whose stature is, for instance, such that twenty 

 per cent of all the individuals of his age are taller than lie, 

 then it is his ideal to train the pupil to that point that all 

 his other measurements come up to the same standard. If 

 all the men who have this particular stature were plotted 

 alone, it would be seen at once that their measurements 

 would be quite different from this assumed standard. This 

 fundamental objection has already been raised by Dr. L. 

 Gulick. 



This assumption is one of the developments of the method 

 of percentile grades. While this method has certain advan- 

 tages in bringing home to the untrained public some of the 

 valuable results to be gained from anthropometric inqui- 

 ries, it is highly objectionable for theoretical studies. It 

 does not explain any fact that cannot be explained just as 

 well and with the tenth part of labor and with greater satis- 

 faction by the method of mean variations, and whenever it 

 has been applied it has proved to be misleading in so far as 

 it suggests always that a certain percentile grade represents 

 certain groups of individuals. For instance, during the 

 period of growth, the average eighty per cent child has been 

 assumed to represent, ''on the average," the same child, 

 which is most assuredly not the case. This method ought, 

 therefore, to be applied with much greater care and for 

 much more limited i)urposes than has been done heretofore. 



1 hope my remarks have served to point out some of the 

 directions in which the theory of anthropometric statistics 

 needs further treatment, and what defects remain to be rem- 

 edied. I have in njy full paper given a number of exam- 

 ples and elaborated the theories and methods which here I 

 could indicate only with a few words. 



