24 American Statistical Association. 



0.079 cm., and a probable deviation of 3.7 cm. This being 

 known, it follows that of tlie 50 per cent of those who exceed 

 the mean 



25 per cent should fall between 118.36 cm. and 122.06 cm. 

 16.2 " " " " 122.06 " " 125.76 " 



6.7 " " " " 125.76 " " 129.46 " 



1.8 " " " " 129.46 " " 133.26 " 



and 0.3 should exceed 133.26 cm., while the remaining 50 per 

 cent should deviate from the mean in a precisely similar man- 

 ner, but in an opposite direction. 



The method admits of still another application. It is 

 evident that in the series just given 122.06 cm. is the height 

 of a girl who is taller than 75 per cent of the girls of her age, 

 and not so tall as the remaining 25 per cent. Her position 

 is thus definitely fixed with relation to the mean. She is in 

 fact the typus or mean of the 50 per cent who exceed the 

 mean of the whole number. The height of such an individual 

 at any age would equal 3I-\-d^ where J/ is the mean height of 

 the age, and d the probable deviation. The values of M-\- d 

 determined for each age in the period of growth are compara- 

 ble, and reveal the growth of the typus of the 50. per cent 

 who exceed the mean of the whole number at each age. The 

 growth of the typus of the 50 per cent who fall below the 

 mean height can be similarly made plain, and, by continuing 

 the process, the law of growth at any given deviation from 

 the mean can be determined. 



The data for these studies can be collected either by the 

 '^generalizing" or '-individualizing" plan. In the former, a 

 great number of measurements is made but once on indi- 

 viduals of different ages, and the measurements classified 

 according to age. In the latter, the same individuals are 

 measured yearly, or oftener, during their period of growth, 

 and the measurements classified also by age. The generaliz- 

 ing method is rapidly and easily carried out, whereas the 

 individualizing method demands for its execution exceptional 

 opportunities and exceptional patience, requiring not only 



