THE NORMAL CURVE 91 



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 q. 



In the example of variability of stature represented 

 by Fig. 5, q is equal to r6 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 



