TYPE AND VARIABILITY 423 



of the race. This is easily determined in the form of a rate 

 per cent by dividing the highest frequency by the total Dumber 

 of variates. 1 The highest frequency in this case is 67, which is 

 over 20 per cent (20.4 +) of the total number of ears measured. 

 This we call its modal coefficient because it indicates the per- 

 centage of the total population that conforms to type in respect 

 to this character. The modal coefficient of some other variety 

 might be quite different, showing that a higher proportion of 

 one variety may conform to type than of another ; or, what is 

 the same thing, that one variety may be more constant and 

 truer to type. The modal coefficient, therefore, is an index of 

 relative conformity to type, a valuable bit of knowledge for 

 purposes of selection. 



Modal coefficient partly dependent upon the scheme of measure- 

 ments adopted. If these measurements had been taken to the 

 quarter inch there would have been twice as many frequencies 

 and each would have been represented by correspondingly fewer 

 ears. The highest frequency, therefore, would have been not 67 

 but approximately half that number, 33 or thereabouts, 

 and the modal coefficient would have been not 20 per cent but 

 near 10 per cent. This being the case, modal coefficients are not 

 directly comparable except when arising from the same system 

 of measurements, or after the coefficient has been divided by 

 the width of the class ; thus, 20 -f- \ equals 10 -+- |. 



For the purpose of comparing the variability of races we use 

 the " coefficient of variability," to be described later. The modal 

 coefficient is chiefly valuable for comparing one type with 

 another within the race, which is all that is required in ordinary 

 breeding. 



Practical value of the frequency distribution, the mode, and 

 the modal coefficient. The practical importance of the informa- 

 tion afforded by these values must be apparent. By means of 

 the frequency distribution the breeder is enabled at any time, 

 when he can secure sufficient numbers, to spread out before his 

 eyes a good and fair representation of the . whole population of 

 the variety or race he is breeding, with respect to any character 

 which he can measure or accurately estimate. 



1 Hy variates is meant the individuals measured (in this case 327 ears). 



