CHAPTER XLIII 

 THE STATISTICAL STUDY OF VARIATION 



STATISTICAL METHODS 



The pioneer workers in the application of statistical methods to 

 biological study were Sir Francis Galton and his leading disciple, Karl 

 Pearson. The use to which Galton and Pearson put their statistical 

 methods appears later in this chapter. For present purposes we may 

 limit our study of biometry to that part of it which has to do with 

 variation. We have already discussed fluctuating variations, the 

 small plus and minus differences that exist between the different mem- 

 bers of the same species or variety. This was the type of variation 

 that Darwin considered the main raw material of evolution. Exam- 

 ples of fluctuating variations are not far to seek. Pearson cites as an 

 illustration of fluctuating variation the number of veins in two sets of 

 beech leaves, each set from a different tree: 



It will be noted that though there were 16- veined leaves on both 

 trees, as well as 15- and 17-veined, the general distribution is quite 

 different in the two trees. In the first tree the most frequently occur- 

 ring type is the 18 -veined leaf, and the other types may be said to 

 fluctuate about this (the "mode")- In the second tree the mode is 

 the 15-veined type and the other types fluctuate about it. It will be 

 seen also at a glance that the types that differ most from the mode are 

 the least frequent and that those nearest the mode are the most fre- 

 quent. 



Some years ago the writer had occasion to study the heredity of 

 scale numbers in the banded region of the nine-banded armadillo. 

 As a preliminary to this study it was necessary to know the degree and 



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