98 BIOMETRY 
falling between certain limits. The frequency of a class 
is the number of variates which it contains. 
The amount of variation shown by a particular 
group of variates is measured by the degree of slope 
of the curve. A flat curve indicates greater variability 
and a steep curve denotes less variability. The flatter 
the curve—supposing the area (the number of 
variates) to remain the same—the further from the 
mode will be the position of the quartile, so that the 
distance of the quartile from the mode may be taken 
as a convenient measure of variability. In a theoreti- 
cally perfect curve the distance of Q and Q’ from M 
is equal. A curve obtained from an actual series of 
variates is never perfectly symmetrical, so that in 
practice the distance of Q and Q’ from M may not be 
quite the same. In such a case the average of the 
two distances is taken as the measure of the variability 
of the material in question, and this value may be 
briefly denoted by the letter g. 
In the example of variability of stature represented 
by Fig. 5, q is equal to 1°6 inches. This amount of 
variability can therefore be compared with other 
values representing the variability in stature and in 
other characters shown by various other groups of 
individuals. This, then, is the first important biome- 
trical result which we have arrived at—the determina- 
tion of a numerical value representing the amount of 
normal variability in any given case. 
A measure of variability more often used than the 
quartile, especially in recent work, is what is known 
as the standard deviation of a normal curve, and may 
