THE CLASSES OF FREQUENCY POLYGONS. 23 



To find j, a , i, "Q, ,'o 



The total range, b, of the curve (along the abscissa axis) is found by 

 the equation 



b = Vfrts + 2) 



Oj and a 2 are the ranges to the one side and the other of t/ ; 



! = y^b da)\ d = a A = VVa ^ 



a 2 = i> a i ; 



nij = ~(s - 2); ?)*! -f m 2 = s 2; 



To solve this equation it will be necessary to determine the value of 

 each parenthetical quantity following the r sign and find the corre- 

 sponding value of r from Table V. It is, however, sometimes easier to 

 calculate the value of y Q from the following approximate formula: 



l/o = r 



(m, 4- 



_L(_J_ _ _L _ JL) 



"With these data the theoretical curve of Type I may be drawn. Fre- 

 quency polygons of Type I are found in biological measurements. 



To compare any observed frequency polygon of Type 

 II \vith its corresponding theoretical curve. 



This equation is only a special form of the equation of Type I in which 

 aj = 3 and ?! = JH,. _ 



As from page 17, ^ = in Type II, 6 = 2cr 4/s + 1 ; since the curve is 

 symmetrical, d = 0, and 



b a rQn + 1.5) 



a = ; nt = J4(s-2); y = - 



The r values will be found from Table V. 



An approximate formula for y is given by Duncker as follows: 



1 



a s - 1 4(s- 2) 



t/ = -- =^ 

 a VZ-ir V'(S 



To compare any observed frequency curve of Type III 

 with its corresponding theoretical curve. 



