EVOLUTION 



387 



deviations, and in our quantitative study of evolution a is 

 termed the standard deviation. Other measures of varia- 

 bility have been devised, some of which are occasionally 

 useful, but for theoretical and practical reasons the standard 

 deviation may be considered the best. It is not hard to 

 find, and it occurs and recurs in all sorts of investigations. 



The following is the rule to obtain it : Multiply the 

 frequency with which each individual type occurs by the 

 square of its deviation from the mean ; add all these pro- 

 ducts together and divide by the total number of in- 

 dividuals. This is the square of the standard deviation. 



For example, in the case of the poppy capsules we 

 have : — 

 {i X (4.84)' + 12 X (3.84)' + 91 X (2.84)2-1- 295 X 



(1.84)'+ 550 X (.84)"' -1- 6i9x(.i6)"' -F4i8 X (i.i6)f 



+ 195 X (2.16)"-^+ 54 X (3-i6)'+ 25 X (4.16)- -I- 5 X 



(5.i6)'-f-3 X (6. 1 6) 2 }-^ 2268 = 2.2 1 7. 



The square root of this is 1.473, or the variability of 

 the wild poppy is measured by 1.473 stigmatic bands. 

 For the individual poppies on p. 383 we have the standard 

 deviations 1.072 and 1.260 respectively. We cannot lay 

 much stress on these last numbers, for the capsules in the 

 individual cases are so few,^ but they illustrate the universal 

 rule that the race is more variable than the individual." 



But the reader must not suppose that we have in tak- 

 ing 2268 poppy capsules reached something peculiar to 

 the wild poppy {Papaver Rhccas), or even to poppies in 

 general. This particular group of poppies was collected 

 from a corn-field nearly at the foot of the southern slope 



^ I am here, of course, only indicating in broad outline the fringe of a 

 very vast subject ; the "probable errors" of all such determinations have to 

 be considered before any valid arguments can be based upon them. 



^ For the beech leaves we have again the individual less than the racial 

 variability. Thus : 



