Hesearches into the theory of probability. 



31 



V. Numerical applications. 



I will apply the above general theory to some examples. 

 Sixth Example. Ntmiber of petals of Ranunculus hulbosus. 

 The following numbers are given by Hugo de Vries and treated by Pearson 

 («Contributions» 1895). 



Class 0 1 2 3 4 5 



Number of petals 5 6 7 8 9 10 

 Frequency 133 55 23 7 2 2 



We will represent this numbers by means of a frequency curve of form B, 

 putting c = 0, OJ = 1, that is using method l:o above. 



We find by a comparison between these numbers and fig. 13 that X has a 

 value, smaller than unity. Placing the provisional origin at the class 0, representing 

 the individuals with 5 petals, we find 



Ih' = 222, 

 \h' = 292. 



More moments it is not necessary to calculate in this case. From these numbers 

 we obtain 



Vj' = + 0.631 



Vg' = + 1.314 = -|- 0.916 



As the value of v^' seems to be not very distant from the value of X, it will 

 be advantageous to use method l:o and, according to the formulae (10) and (17), 

 we then obtain 



X = v/ = -f 0.631, 



^2 ^ + 31.5, 



so that 



From the table of Bobtkewitsoh we obtain through interpolation the following 

 values of ^■)^{x) corresponding to X = 0.631. The values of A({) and A^rjj are obtained 

 by taking the differences: 



X 









0 



+ 0.632 



+ 0.532 



+ 0.532 



1 



4- 0.336 



— 0.196 



— 0.728 



2 



-f 0.106 



— 0.230 



— 0.034 



3 



-f- 0.022 



— 0.084 



+ 0.146 



4 



-f- 0.003 



— 0.018 



4- 0.066 



5 



-j- 0.000 



— 0.003 



+ 0.015 



