24 STATISTICAL METHODS. 



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

 by the formula 



a = o- 4 ~ ^i. = a 1 ~/ 2 (for Type III). 

 2 VjSj 



a a Of. J> + ] 



Also, p = ==-; 2/o = 



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

 Appendix. 



To compare any observed frequency curve of Type IV 

 with its corresponding theoretical curve. 



This is the commonest type of biological skew curves. 



y = y (cos9} 2m .e- vd . 



9 is & variable, dependent upon x as shown in the equation 

 x = a tan 9. 



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

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

 zero ordinate is at M md; or at a distance m X d from the mean. 



4 



/t/ZiIs(s 2) i/07 



v ^- i 1, with the opposite sign to p B ; 



0(arc of circle) = ^^; 



^__ L _ 



a / T 



2/o = - V 5Z 



angle whose tangent is . 



* 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 <,&* 



Vo = ~ 



a /7T 



/ (sin 

 t/0 



9fe vd dd 



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

 lus. 



