18 



STATISTICAL METHODS. 



i 0; 



* = v* - rS -f- 1; 

 a = r 3 3?'iK 2 -f 



Also, 



= 



and 



F = 6 + 3/3, - 2/J 2 = the "critical function." 

 Now the classification of any empirical curve depends upon 

 the value of its critical function, F. 



,(/?i> 0, curve is of Type I. 



When dispositive and \ ' '.* crn TT 



] //! = 0, ^ 2 < 3, curve is of Type II. 



ft i > 0, yS a > 3, curve is of Type III. 

 fj l = 0, /Jo = 3, curve is normal. 

 " F is negative and fii > 0, ^ 2 > 3, curve is of Type IV. 

 An important relation to be referred to later is 



6(/? a - A - 1) 



~T~ "' 



in which s is an unknown, positive number. 



Jf 



5 i 



THE NORMAL CURVE. 



The normal curve is symmetrical about the mode ; con- 

 sequently the mode and the median and mean class coincide. 



The mathematical formula of the normal curve, a formula 

 which one does not have to understand in order to make use 



of it, is 



<x 



