Volume II 



NOVEMBER, \'.H)-2 



Ni>. 1 



BIOMETEIKA. 



ON THE SYSTEMATIC FITTING OF CURVES TO 

 OBSERVATIONS AND MEASUEEMENTS. 



l.iERAF.V 



PART II.* .;. 



:a 



By KARL PEARSON, F.R.S., University College, London. 



CONTENTS. 



(9) On the Fitting of Normal Frequency Distribiitions wlien a part only of thc 

 Frequency is given ........ 



Illustration V. American Trotting Horses .... 



(10) On the Moments of Trapezoidal Areas 



(11) On the Fitting of Parabolic Cm-ves of any order to given Data 

 (a) Method of Least Squares 



(12) (6) Method of Moments 



(13) Illustration VI. Thiele's Patience Statistics .... 



(14) Illustration VII. Italian Marriage Statistics .... 



(15) General Conclusions ......... 



Paus 



1 



2 



7 



9 



9 



12 



16 



20 



21 



(9) Illustration V. In the previous illustration we have fitted the best 

 curve not to the ordinates, but to the logarithms of the ordinates. This method 

 was forced upon us by the complexity of Makeham's formula. It will clearly give 

 goüd resiilts in many cases where it inight be difficult to calculatc the momcnts 

 of the ordinates of the curve, but in whioh the raoments of the lotrarithnis of the 

 ordinates follow quitc easily. For example in curves of the type y = e-'^'-^' we 

 shall often introduce considerable simplicity into nur work without loss of practical 

 efficiency by fitting to the data a curve Y=f(,r), where F=logy. In particular 

 * Part I. was publishcd in Vol. i. p. 265. 



Biometrika ii 1 



