60 American Statistical Association. 



theory is true, the probable deviation is a measure of the 

 degree of deviation of individuals from tlieir physical type. 

 The probable deviation contains the Error of Observation as 

 well as the Physiological Difference of the individual from 

 the type. The Error of Observation, in a large series of meas- 

 urements, is insignificant. The probable deviation may there- 

 fore, witliout any error of importance, be considered as tlie 

 physiological difference betvv^een the individual and the type. 

 The comparison of the probable deviations from the aver- 

 age height standing of the school children in the Freiburg 

 School District (measured by Geissler and Uhlitzsch) and 

 the St. Louis school chiklren reveals a difference of only a 

 few millimetres, although St. Louis children are taller tlian 

 Freiburg children. It follows that the physiological differ- 

 ence between individual school children and the physical 

 type of their sex and age is essentially the same Avhere the 

 differences between the children compared are not greater 

 than those existin(T between the St. Louis and the Freiburo^ 



to O 



children. 



The probable deviation at different ages is found to vary 

 with the quickness of growth as measured by the relative 

 annual increase of average height, weight, etc. Hence, the 

 physiological difference between the individual children in 

 an anthropometrical series and the physical type of the series 

 is directly related to the quickness of growth. 



It is much disputed whether median or average (arithmet- 

 ical mean) should be employed as the type value. The dif- 

 ference between the median and the average values in this 

 investigation is relatively small, indicating that the median 

 value, which is obtained with comparatively little labor, may 

 be used in place of the average, where the material is as large, 

 and of the same nature, as that analyzed by me. 



It is pointed out that the comparisons now often made 

 between the type-children of the schools of different cities 

 and countries cannot be justified, unless it is shown that the 

 school populations from whicli these types are drawn are 



