34 STATISTICAL METHODS. 



6 (arc of circle) = rr^,* 



f ^_l^ 



<f)= angle whose tangent is . 

 s 



To compare any observed frequency polygon 

 of Type V with its corresponding- theoretical 

 curve. 



y=y x~~ p e~ r/x . 

 To find p solve the quadratic equation 



and take the positive root. 



D ^. 



T( P -iy JKF 1 *)' 



To compare any observed frequency polygon 

 of Type VI with its corresponding theoretical 

 curve. 



1 q 1 and q 2 + 1 are the two roots of the equation 



s 2 



' where U 9i) and sare negative; 



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

 usually the case, a is greater than 2. The exact value is given by 

 Pearson as 



jf 



(sin 0fe re d0 



the formula for reducinc which is to be gained from the integral oaJ- 

 culus. 



