X X X 1 1 X XXIV] Introtluetion rl vii 



For the <j>'s we have from p. 217, 



<fr = -298,125, fa = '077,7658, fa = - '029,3748, fa . - (>:, 1 M',-2 1 

 Thus the second part Y n ' ofy(n, r, p) equals 



-298,125 -077,7658 _ -029,3748 _ -05 1 ,:{-,:> 1 



9 <J 2 ! :1 !' 



= 1*0340,3695. 

 Hence y (10, -55, -7) 1*086,773 x 1-0340,3695 



= 1-123,763, 

 or if the total frequency be, as in our table, 1000, 



y(10, -55, -7) = 1123-763. 

 The value given in Table XXXII (p. 192) is 1123-76. 



These results will give the student confidence that a good value may be easily 

 obtained for any ordinate for n = 10 and upwards from Table XXXIII. 



The reader will observe that in Table XXXII we have recorded the ordinates 

 at intervals of "05 and the standard deviations of no less than 270 curves distributed 

 over the /8i, /3 a plane. Given therefore any frequency distribution with its & and 

 2 equal to those of one of these curves, and its total frequency reduced to 1000, it 

 should have its ordinates nearly the same as those of the corresponding y(n,r,p) 

 curve provided we place mean upon mean, and adapt our ordinate interspace to the 

 interspace in terms of the new standard deviation. 



Illustration (iii). For certain data the following values were determined, the 

 number of observations being 1086 : 



Mean = 22-8361, a = 13'5078, 

 & = -6783, #8 = 3-7342. 



Approximately these values of the /3's will be found between the columns for n = 13, 

 p = '5 and p = "0, by interpolating linearly in the ratio '19 to -81. We thus find 



& = '6761, a = 3-7412, 

 well within their probable errors from the observed quantities. 



Interpolating also linearly for the other constants we find from Table XXXII, 



p. 195, 



Mean = '4841 x -81 + "5834 x 19 = '5030, 



Mode = -5908 x '81 + '6880 x -19 = '6093, 

 Standard Deviation = "2279 x '81 + '1 !>04 x -1J) = 2i>-2:.. 

 Distance from Mean to Origin in terms of S.D. 



01 i<>_ 9-9765 



-2279 X 81 + -1994 X ] 



