THE CLASSES OF FREQUENCY POLYGONS. 23 



of which one does not have to understand the development 

 in order to make use of it, is 



This formula gives the value of any ordinate y (or any class) 

 at any distance x (measured along the base, X, X', of Fig. 5) 

 from the mode, e is a constant number, 2.71828, the base 

 of the Naperian system of logarithms, n is the total area 

 of the curve or number of variates, and a is the Standard 

 Deviation, which is constant for any curve and measures the 

 variability of the curve, or the steepness of its slope. 



To compare any observed curve with the theo- 

 retical normal curve we can make use of tables. For 

 the case of a polygon of loaded ordinates the theoretical fre- 



x 

 quency of any class at a deviation from the mean can be 



taken directly from Table III. Here is the actual devia- 

 tion from the mean expressed in units of the standard devia- 



tion, and the corresponding ordinate, y being taken as 



2/o 

 equal to 1, and a is the standard deviation. 



For the case of a polygon built up of rectangles represent- 

 ing the relative frequency of the variates, Table IV gives 

 immediately the theoretical number of individuals occurring 



between the values x=Q and x= . By looking up the 

 given values of the corresponding theoretical percentage 



of variates between the limits x=0 and x= db will be found 



a 



directly. The ratio may be called the Index of Abmodality. 



The normal curve may preferably be employed even when 

 & is not exactly equal to 0, nor /? 2 exactly equal to 3, nor F 

 exactly equal to 0. Use the normal curve when 



and 



