THE CLASSES OF FKEQUENCY POLYGONS. 17 



as a zero point ; then the departure of all the other classes 

 will be - 1, 2, - 3, etc., and + 1, -f 2, -f 3, etc. 



Add the products of all these departures multiplied by the 

 frequency of tbe corresponding class and divide by n\ call 

 the quotient v\. 



Add the products of the squares of all the departures multi- 

 plied by the frequency of the corresponding class and divide 

 by n\ call the quotient v*. 



Add the products of the cubes of all the departures multiplied 

 by the frequency of the corresponding class and divide by n\ 

 call the quotient v*. 



Add the products of the fourth powers of all the departures 

 multiplied by the frequency of the corresponding class and 

 divide by n\ call the quotient r 4 . Or, 



Vm) 

 - = departure of V m from mean. V m being 



known, M may be found [M = Vm + v\\\ * 



_ 2( v- v m y 



The values r lf ?' a , v 3f r 4 , are called respectively the first, 

 second, third, and fourth moments of the curve about Vm. 



To get the moments of the curve about the mean, either of 

 two methods (A or B) will be employed. Method A is used 

 when integral variates are under consideration ; method B 

 when we deal with graduated variates. 



(A) To find moments in case of integral variates: 

 Hi = 0; 



Mi = r* v^\ 



ju 3 r 3 Srirt -f 2ri s ; 



J*4 = f 4 4^i^ 3 + 6^iV a 3^! 4 . 



(B) To find moments in case of graduated variates : 



* This is the short method of finding M referred to on page 14. 



