36 GENETICS IN RELATION TO AGRICULTURE 
The significance of the normal curve as an index of variation is based 
on the conception that the area within the curve represents an indefinite 
number of individuals and that the constants of the curve indicate the 
distribution of these individuals with respect to a given character. If 
in any curve (Fig. 16) the perpendicular erected at M divides the area_of 
the curve into two equal parts, this line is the median and the point MW 
represents the average or mean of all the values from which the curve is 
constructed. The perfect symmetry of the normal curve causes the 
median to coincide with the mean and the mode; but in actual cases 
FAN 
i M Q, Q, M Q, 
Fic. 16.—A normal curve divided TIic. 17.—A normal curve of exactly the 
into quartiles by the perpendiculars same area as the curve in Fig. 16, but with flat- 
erected at M,Qi,Q3. ter slope and correspondingly greater breadth. 
The distribution pictured by this curve pre- 
sents a greater range of variation than in 
Fig. 16 as is indicated also by the value of Q. 
these three values will not coincide because the curve will not be sym- 
metrical. If a perpendicular be erected in either half of the curve at 
such a distance from M that it divides the area enclosed by the median, 
the base and half of the curve into two equal parts, the distance of such 
a perpendicular, Q; or Q; from J is the quartile, g. Then in the normal 
curve g = MQ: = MQ;. Now the slope of the curve is an index of the 
amount of variability. The steeper the slope supposing the area (the 
number of individuals) to remain the same, the nearer to the median 
will be the position of the quartile and hence the position of the quartile 
is also an index of variability (Fig. 17). Since curves constructed from 
actual distributions are never symmetrical, in practice the index taken is 
nt, However, the measure of variation in common use zs the standard 
deviation, «, which in the normal curve represents a distance from the median 
q 
equal to 
q 0.6745 
Requirements of Biometrical Study.—The data for statistical analysis 
are obtained by counting, by measurement, or by arbitrary graduation 
of continuous differences like degree of pigmentation. In order that such 
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