24 STATISTICAL METHODS. 



The range at one side of the mode is infinite; at the other is found 

 by the formula 



a = <r 4 ~ fe. = cr 1 ~ /*" (for Type III). 

 2 Yfr A 



a a a. ]? + ! 



Also, 



d A ' a ' 



The value of r corresponding to p + 1 can be got from Table V, 

 Appendix. 



To compare any observed frequency curve of Type 

 with its corresponding theoretical curve. 



This is the commonest type of biological skew curves. 



y = 

 is a variable, dependent upon x as shown in the equation 



x = a tan 0. 



The factor (cos 0) 2m following y indicates that the curve is not calcu 

 lated from the mean ordinate (M), or the mode (M d), but tliat the 

 zero ordinate is at M md\ or at a distance m x d from the mean. 



a = - |/ 16(8 -l)-^*-^; m = Y 2 (s + 2); 



md = VW(S - 



v= - - - - , with the opposite sign to MI ; 



ir6 



0(arc of circle) = 



180' 

 (cos $Y* 



r e 3s 12.9 



2/o = 'V s- 



v 



= angle whose tangent is . 



s 



* The foregoing value is approximate and is applicable when, as is 

 usually the case, s is greater than 2. The exact value is given by Pear- 

 son as 



a e \w 



Vo = 



a /TT 



/ (sin 0)' 



t/0 



R e v0 d9 



the formula for reducing which is to be gained from the integral calcu- 

 lus. 



