32 STATISTICAL METHODS. 



To find 1 19 1 2 , m l9 m 2 , y Q . * 



The total range, Z, of the curve (along the abscissa axis] 

 is found by the equation 



1= 



Zj and 1 2 are the ranges to the one side and the other of t/ ; 



2 . a; 



1 . m 2 



=s 2; 



To solve this equation it will be necessary to determine 

 the value of each parenthetical quantity following the F 

 sign and find the corresponding value of F from Table V. 

 It is, however, sometimes easier to calculate the value of y Q 

 from the following approximate formula: 



_n (m 1 + m 2 +l)\m 1 + m 2 12 

 I \/27tm l m 2 



_J1___L\ 

 2 m\ m 2 / 



With these data the theoretical curve of Type I maybe 

 drawn. Frequency polygons of Type I are often found in 

 biological measurements. 



To compare any observed frequency polygon 

 of Type II with its corresponding theoretical 

 curve. 



This equation is only a special form of the equation of Type 

 I in which Z X =Z 2 and m 1 = m 2 . 



As from page 22, ^ = in Type II, l=2a\/s+l; since the 

 curve is symmetrical, D 0, and 



t/ ON n F(m+1.5) 



m=i(-2); 7/ =- A -f-. 



The F values will be found from Table V. 



