158 Pearl and Surface. 



shown by examples. Thus a plant with a mean quintile position not 

 greater than 1'8 cannot have its fourteen observations more widely 

 distributed than the following example. 



Quintües I II III IV V 



Frequency 11 1 2 



The mean of this distribution is 1-786 and the standard deviation 

 is 1'520. On the other hand the widest possible distribution of the 

 measurement of a plant having a mean of 3'0 is given by 

 Quintiles I II III TV V 



Frequency 7 () 7 



The mean of this distribution is 3'0 and the standard deviation 

 is 2-00. 



It is thus evident that the plants which are medium sized may, 

 because of this very fact alone, have larger standard deviations than 

 either the small plants or the large plants. The question with which 

 we are concerned is whether the difference between the variabilities of 

 the extreme plants and the medium sized plants is greater than can be 

 accounted for by the differences in their means. That is are the plants 

 in the end classes actually less variable after making allowance for the 

 difference in the means? 



What we wish to know then is the most probable standard devi- 

 ation of groups of plants whose means fall within the classes of I'D to 

 1"8, 1'8 to 2 '6, etc. One way of determining this is to write down 

 every possible combination of 14 figures wliich when distributed in five 

 classes or less will give a mean value between 1"0 and 1'8. An example 

 will make tliis clear. 



Quintiles 



The mean of each of these distributions is less than TS. It 

 requires some time to write out all the possible combinations but it is 

 not difficult to do. Similarily the various combinations having means 

 between 1"8 and 2' 6 and those between 2*6 and 3 "4 may be written 

 out. The values in the last two classes will be the reverse of those in 

 the first two classes. 



