THE CLASSES OF FREQUENCY POLYGONS. 23 



To find x , a a , m^ w a , y . 



The total range, 6, of the curve (along the abscissa axis) is found by 

 the equation 



aj and a a are the ranges to the one side and the other of y Q ] 

 a^ = ^b ds); d = irA = VV a . A\ 



a a = 6 



y Q = _ . I1L1 L_ZI2 m -vi ' " ' "' . 



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: 



(m, m*^ gh ^a e i m a n^ wi a ^ 



O I/27TWI J 



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 with its corresponding theoretical curve. 



-*(- D" 



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

 a! = a and ??*! = m a . 



As from page 17, /3j = in Type II, b = 2o- V -f 1 ; since the curve is 

 symmetrical, d = 0, and 



b & T(m + 1.5) 



- - - 



The r values will be found from Table V. 



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



s - 1 



1/27T V(s + l)(s - 2) 



To compare any observed frequency curve of Type III 

 with Its corresponding theoretical curve. 



