THE STATISTICAL STUDY OF VARIATION 35 
From Fig. 15 it is evident that as n becomes larger the straight lines of 
the polygon more closely approximate the normal curve. 
The normal curve is perfectly symmetrical because it represents the 
distribution of an indefinitely large number of items and it assumes all 
causes to be of equal strength or value. It is assumed that certain 
biological frequency polygons should simulate this curve for these reasons. 
It is probable that the environment of any organism is made up of a 
large number of factors each of which may vary around a mean independ- 
Fig. 15.—Polygons representing expansion of the binomials (a + b)® and (a + b)?° as 
compared with the normal curve. 
ently of the others. Now if a frequency polygon is to be made regarding 
a character of a population composed of individuals alike in zygotic 
constitution, such as a field of potatoes of the same variety, the differences 
found in the development of any character are due wholly to these en- 
vironmental factors. Hence it is likely that the mean of the distribution 
is made up of observations on individuals upon which an equal number 
of favorable and unfavorable forces have acted and the deviates are those 
upon which a greater or less number of favorable or unfavorable forces 
have acted. But in sexually reproduced allogamous species the in- 
dividuals are not alike in zygotic constitution. Moreover, the causes 
affecting a given character may have an unequal mass effect according to 
ecological conditions. Either of these factors may cause a high degree of 
asymmetry in a polygon of variation. Graphs in which the mode is 
rather far removed from the mean are called skew polygons or curves. 
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