THE CLASSES OF FREQUENCY POLYGONS. 29 



(1) 2/=: 



where I is the half range and 



2 =3.75(3A 2 ->1 ); 

 also, 



= = - 



To find m arrange the frequencies in the usual manner 

 (p. 26) and find the logarithm of each; their sum is equal 

 to ra . Making the class situated at the middle of the 

 range 0, find the deviation of each of the other classes frcm 

 this class. The algebraic sum of the product of the loga- 

 rithms by the deviations gives m r The second moment 

 about the same zero point gives m 2 . Or, 



Substituting in (1) we get a numerical quadratic equation 

 which can be put in the form 



_ 



If the normal curve be y=z e 2<? 2 

 (3) y 



whence, by comparison of right-hand expressions in equa- 

 tions (2) and (3), 



Then the required normal curve is 



^y^v 



(Pearson. 1902 m .) 



