DISTRIBUTION OF COLLEGE CREDITS 405 



the cases lie. It means that a student taken at random from a class 

 of one hundred has one chance in four of falling above the middle 

 group. It means that if we represent the ability of this group by C, 

 we know precisely what an instructor means when he gives a student 

 that grade. He means that the ability of the student in his course is 

 greater than that of one fourth of the course and less than that of an- 

 other fourth of the course. This median group ought to be the largest, 

 for it is where most human beings fall, as shown by the height of the 

 probability curve. 



We can not indicate real distinction, however, unless we subdivide 

 the upper quartile. We can do this arbitrarily or we can turn to a 

 table of values of the normal probability integral.' Here the extreme 

 ability is called 3. The point of the vertical line which separates the 

 median group from the inferior group is .68. Half way between 3 and 

 .68 is 1.84. Accepting this as the division point for the upper and 

 the lower quartile, we find at the upper end of the surface of distribu- 

 tion three per cent, of the whole, and at the lower end three per cent. 

 If we indicate the five sections, from the upper end to the lower, by 

 the symbols A, B, C, D, E, we have the following distribution of 

 grades : 



Per Cent 



A 3 



B 22 



C 50 



D 22 



E 3 



If, on the other hand, we assume that the distribution of abilities of 

 college students is not normal, but skewed, the following percentages 

 for each grade would more nearly represent the facts: 



Per Cent. 

 A 2) 



B isr 



50 



As variation in the abilities of those who elect a given course is sure 

 to occur from year to year, some would prefer an elastic definition of 

 the grades; for example: 



Percent. 



A 0-6 



A 15-21 



C 45-55 



D 20-28 



E 0-10 



• A table of values of the normal probability integral is found on page 148 

 of Thorndike's "Mental and Social Measurements." In Science, 712, 243, Max 

 Meyer uses this basis for dividing the probability surface. 



