1919] Frost: Mutation in Matthiola 149 



In the calculation the deviations are taken from zero, and with 

 these small numbers of samples the percentages are not thrown into 

 classes; it suffices, then, to square each number of "successes," divide 

 by the corresponding total of individuals, add the quotients, and 

 divide by the grand total of individuals, correcting this weighted 

 mean squared deviation by subtracting the square of the weighted 

 mean percentage (percentage of grand total). If s is the number 

 of successes and n is the total number of individuals in the sub- 



sample, and M is the weighted mean percentage, then M= — , and 



2« 



X- 



per cent , —, ,^ 



iVi". 



Table 39 gives, for the most important comparisons of heredity 

 percentages, the total number of progeny (A'), the number of cultural 

 groups or (with the first line for each type) the number of parents (/), 

 the average size of the groups of progeny {n), and the mean per- 

 centage of the mutant type (p). This serves as a summary of some 

 of the most important statistical data already presented relating to 

 the inheritance of these types, and also shows the basis of the remain- 

 ing part of this table and of table 40. For comparison of actual and 

 theoretical standard deviations the theoretical value has been calculated 

 from the actual percentage as given in this table. For comparison of 

 means (table 40) the percentage of the corresponding total (p,,) 'i^s 

 also been used, this theoretical standard deviation being the second in 

 the table in the cases where the two values are not identical. 



Since small changes in a percentage have little effect on its 

 theoretical standard deviation, we are fairly well justified in taking 

 the latter, as calculated from the actual percentage in each case, to be 

 the ''population" value. Consequently, the difference between the 

 theoretical and actual standard deviations has been expressed in each 

 case as a multiple of the probable error of the theoretical value. 



Aside from the last line for crenate-leaved, where there is an 

 obvious artificial reason for high variability, there is no very significant 

 difference except with slender. In this case, the deviation of 5.7 times 

 the probable error (line 1) is probably largely due to the genetic 

 differentiation of "extreme" and "ordinary" parents suggested by 

 their appearance and hj the wide difference in the heredity per- 

 centages; the differences become moderate when the progeny of the 

 two classes of parents are separated. 



