The Measurement of Variation 43 



desirable, however, to treat plants in groups by means of 

 statistical generalizations. 



Type. In the study of any group of plants, called a 

 " population, " whether it be corn, wheat, the ray-florets 

 of daisies, or what not, the breeder has in mind a certain 

 type around which the individuals tend to center. 



The corn breeder has in mind a certain length of an ear 

 of corn which is his ideal type. He chooses ears of this 

 length and plants them in his plat, and at harvest time 

 what does he get ? Not all ears of this length, but ears 

 ranging above and below this length. The offspring will 

 be distributed, in all probability, above and below this 

 parental type and may possibly reach the upper and lower 

 limits of the race. There will be a group near the average 

 which will contain a larger number of individuals than 

 any other and thus we have another conception of type. 

 There is the ideal parental type which the breeder has in 

 mind, and another type, probably different, shown by the 

 offspring. To find the latter, the ears of corn are' care- 

 fully measured and their average length determined. 

 This average constitutes a concrete mathematical expres- 

 sion for the type of the offspring. 



Biometrical expression of variability. The amount and 

 range of variability may also be well expressed statistically. 



As an illustration, a number of pea plants were measured 

 and their height was found to range from 5 to 30J inches. 

 A few were short and a few were tall, but most of the plants 

 were of average height. For the sake of convenience, the 

 plants having similar measurements were placed together 

 in one class. When all the results had been brought 

 together they appeared as in the following table : 



