EXAMINATIONS, GRADES AND CREDITS. 



37i 



portional to the numher of women falling within the limits of an 

 inch. Thus 16.3 per cent, were between 63 and 64 inches; 11.5 per 

 cent, between 64 and 65 inches, etc., only two falling between 70 and 

 71 inches. The women near the average tend to differ in height by 

 about 1/2 00th of an inch, while the tallest or shortest of the thousand 

 tend to differ by half an inch or more. This curve, showing the 



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1 



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11 <v . ^ , ^ - ^ T >-*^ 



HH 1 1 I . I ! 1 1 1 



Fig. l. Distribution of Stature of Women in Inches. 



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distribution in height, corresponds closely with the fainter and more 

 regular curve on the figure which represents the distribution of events 

 due to a large number of small causes equally likely to affect them 

 in one of two ways, the curve of error of the exponential equation 

 whose properties have been discussed by Gauss, Laplace and other 

 mathematicians. 



If the performances of students in examinations are assumed to 

 vary in the same way as their height, then we can if we like place 

 them in classes which represent equal differences. Thus by the Har- 

 vard-Columbia method of grouping into five classes, if we put half 

 the men into the middle class, C, and let B and D represent an 

 equal range, we should give about 23 per cent, of both B's and D's 

 and about 2 per cent, of both A's and F's. This, however, gives too 

 few men in the A and F classes for our purposes. If we make the 

 range of the unit 20 per cent, smaller, we obtain the distribution 

 shown in Figure 3, according to which of ten men four would 

 receive C, two B, two D, one A and one F. It departs slightly from 

 the theoretical distribution, but certainly not so much as the theoretical 

 distribution departs from the actual distribution. It appears to be 

 the most convenient classification when five grades are used; one in 

 ten being given honors and one in ten being required to repeat the 

 course corresponding fairly well with the average practise and being 

 a convenient standard. 



