CHAPTER XXV 
BIOMETRY (THE STATISTICAL STUDY OF VARIATION 
AND HEREDITY) 
THE STATISTICAL STUDY OF VARIATION 
H. H. Newman 
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: 
Number of veins................ 13, | 14] 15 | 16 | 17 | 18 | 19 | 20 
INUMDER Of LEAVES a sates ss a coresacecinna sel Ta aac tenanys fina sectaltetdseue | nies aoe fastball gcouesad|Maxoeannl eames 
PTS ECO Cis ace sesnncaveny oan shavacnoniemecaleree I 4] 7] 90| 4] 1 { 26 
Second tree: segassccaamean ess 3 Bk Oe] BF 26) cape sae eares 26 
Ota ee encsias aspen ates | 3 4 | 10 2} 9| 9| 4| z| 
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 19-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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