VARIATION AND HEREDITY 7 



tween the frequency of a particular variation and the 

 amount of its deviation from the mean stature of the 

 group. Among the measurements of 2,600 men, taken at 

 ramdom (that is, as they come and without any conscious 

 effort to select only the tall or the short), there are 1 of 

 4 ft. 8 in. ; and 1 of 6 ft. 8 in. ; 12 of 5 ft. ; and about 12 of 

 6 ft. 4 in. ; that is, equal numbers at equal distances from 

 the mean of 5 ft. 8 in. This illustrates that when the 

 frequency and the magnitude of the variations are 

 registered, they show what is called the normal curve of 

 frequency. This can be illustrated more clearly by ref- 

 erence to the following table of the heights in centimeters 

 of 1,000 ten and one-half year old American school boys. 7 



Between 109 and 113 centimeters tall, 2 boys. 



113 " 117 " " 5 " 



117 " 121 " " 25 " 



121 " 125 " " 97 " 



125 " 129 " " 199 " 



129 " 133 " " .....255 " 



133 " 137 " " 228 " 



137 " 141 " " 126 " 



141 " 145 " " 49 " 



145 " 149 " " 11 " 



149 " 153 " " 4 " 



When this material is plotted in graphical form the 

 distribution of stature is as represented in figure 1, 

 letting the distance of each horizontal line from the 

 base stand for the number of boys. Now if we were 

 to draw a smooth curve through the tops of the columns 

 we should have a bell shaped curve of the type shown in 

 figure 2. This illustrates graphically what we meant 



7 Thorndike, E. L. Individuality, p. 8. 



