VARIABILITY OF A SINGLE CHARACTER 117 



All this means that in choosing schemes of measurements 

 and assigning values to class groups care must always be taken 

 that the assignments are fair as between groups, in which case, 

 the distribution will be smooth and fairly representative of the 

 population, all of which is far more important than is extreme 

 accuracy in individual measurements. 



Suggestions as to numbers. The number of cases needed is 

 a rather difficult matter without getting involved in the question 

 of probable error, ^ which is too complicated for consideration 

 here. In general, large numbers are necessary. For work in 

 com 200 to 300 give good results, and in most ordinary prob- 

 lems this number answers very well. For extreme accuracy and 

 for certain classes of problems much larger numbers are needed, 

 but problems of that character involve considerations that are 

 outside of our present purpose,, which is to acquaint the student 

 with the ordinar)' operations of statistical work. 



Suggestions as to taking samples. When a comparatively 

 small number of individuals (200 to 500) is to be taken as rep- 

 resentative of the entire race to which they belong, it is neces- 

 sar)' that the sample be carefully chosen. It should be what is 

 called a " random sample." That does not mean a careless 

 sample taken without regard to obvious differences, but it means 

 a fair and representative sample. If the corn, for example, is 

 husked and in a pile, there would be no better way than to 

 shovel up the sample, taking whatever the scoop might deliver. 

 But if the corn is in the sta.lk, the matter is different. If the 

 ears are to be picked off, they must all be taken for a given 

 area, for no man can be trusted to sort fairly, and areas enough 

 must be taken to fairly represent the field. 



Again, suppose one portion of the field is good, but that the 

 com in the low ground is partially drowned out, and the ears, of 

 course, are small. In this case the proper proportion of the poor 

 corn must be included or the result can be considered as repre- 

 sentative only of the good portion of the field. 



1 " Principles of Breeding," pp. 437-440. 



