Researches into the theory of probability. 



21 



Fourth Example. Distribution of frequency in the cephalic index of 22505 

 Swedish recruits. 



In an important work ■» Anfhropologia suecica» M. Retzius and Fürst have 

 studied the Swedish recruits in the years 1897 and 1898 in different respects of 

 interest for statistical anthropology. From this work I take out the following 

 numbers relating to the cephalic index (»Schädelindex») of 22505 Swedish recruits 

 in the year 1897. 



Cephalic index 



65.5 



67.5 



69.5 



71.5 



73.5 



75.5 



77.5 



Class 



— 6 



— 5 



— 4 



— 3 



— 2 



— 1 



0 



Frequency 



12 



87 



510 



1952 



4346 



6039 



5050 



Cephalic index 



79.5 



81.5 



83.5 



85.5 



87.5 



89.5 





Class 



+ 1 



+ 2 



+ 3 



+ 4 



+ 5 



+ 6 





Frequency 



2822 



1172 



377 



94 



31 



13 





The class range is here equal to two integer cephalic indices, the above 

 numbers being the sum of the frequencies relating to two consecutive cephalic in- 

 dices in the table of Retzius and Fürst. The provisional origin is taken at 77.5. 

 The reckoning according to the given scheme gave the following values of the 

 parameters: 



[j.o = 22505, 



h = — 0.721, 



a = -|- 1.644, 

 ßj = — 0.0104, 

 ß, = + 0.0151. 



Hence the mean was equal to 76.058, and the standard deviation expressed in 

 cephalic indices was 3.088. 



The above results were obtained with the uncorrected values of the moments. 



In fig. 11 is shown the graphical comparison between theory and observation. 

 The agreement is very perfect as may be expected from such an extensive material. 



It must be remarked that this treatment of the beautiful material relating to 

 the cephalic index of Swedish recruits has a cjuite provisional character. In the 

 above calculation 22 individuals with extreme index values have been excluded. 

 Their retaining claims a fuller discussion of the problem than is for the moment 

 possible for me to give. 



Fifth Example. Typhoid fever in Lund 1905. 



As a last example of frequency curves belonging to type A, I take a 

 case from medical statistics, namely the typhoid fever in Lund in this year. The 

 following numbers are taken from an official account on this fever, which appeared 

 in »Lunds Dagblad» in September this year. As the numbers fluctuated rather 

 much from one day to another, I have taken together the results for three coxi- 



