406 



Plant-Breeding 



and then extracting the square root of the quotient. The 

 formula is : 



or = 



M = 37.94 cm. 



Av. Dev. = 11.4712 cm. 



cr = 14.9789 cm. 



Performing the operations indicated by this formula, we find 

 the standard deviation in our problem to be 



112183.2000 

 500 



14.9789 cm. 



The squaring of the deviations has the effect of exaggerating 

 the departures of the extremes, and thus the standard deviation 

 is always greater than the average deviation, so that the two 

 are not comparable. For the practical breeder the one is just 

 as good as the other and whether he employs the average devia- 

 tion or the standard deviation is of little practical importance 

 so long as he is consistent in the use of one to the total exclu- 

 sion of the other in the same piece of work. 



Finding the mean and the standard deviation by the " short 

 method." Where large numbers are used, the derivation of the 

 mean and the standard deviation by the method presented 



