THE CLASSES OF FREQUENCY POLYGONS. 31 



separated from each other by a certain distance D; or D = 

 mean mode. Asymmetry is measured by the ratio a= . 



If the mean is greater than the mode, skewness is positive; 

 if the mean is less than the mode, skewness is negative. D, 

 and hence skewness, may be calculated when the theoretical 

 mode is known (see pages 13, 14, and below). 



In Types I and III skewness is measured also by the 



raVo -WA- where 



5/? 2 6ft 9 is positive, a has the sign of // 3 ; if negative, 

 a has the opposite sign to /z 3 (Duncker, '00 b ). 



In Type I, .-Jv* 



" " III, a=%\/J l = 3 -, where the sign is the 

 + 2\/>2 3 same as that of p 9 . 



" " IV, a= 



,, 

 P 



since p 4 is the positive root of the quadratic: 



p is readily found. 



in Type VI, a= 



, 



where (1 qj and (q 2 +l) are tlie two roots of the equation 



s 2 

 2 _ o I . 



" h 



To compare any observed frequency polygon 

 of Type I with its corresponding theoretical 

 curve. 



