170 Prof. Karl Pearson on Deviations from the 



from the most probable 



P=-5586. 

 In 56 cases out of a hundred such trials we should on a 

 random selection get more improbable results than we have 

 done. Thus we may consider the fit remarkably good. 



Illustration V. 

 The following table gives the frequencies observed in a 

 system recorded by Thiele in his Forelaesinger over almindelig 

 Jagttagelsedaere, 1889, together with the results obtained by 

 fitting a curve of my Type I, The rough values of the 

 moments only were, however, used, and as well ordinates used 

 measure areas : — 



Groups. 



Observed 



Cur re m x . 



e. 



- -18 



- 2*32 

 + 6-48 

 4-10-19 

 -21-64 

 4- 7-10 



- 3 10 

 4- 1-41 

 4- 2-25 



- 1 47 



- -06 

 4- 2-96 



- 2-12 

 4- -06 

 4- -34 

 4- -10 

 4- 



e 3 . 



•0324 



5-3824 



41-9904 



103-8361 



468-2896 



50-4100 



9-6100 



1-9881 



50625 



21609 



0036 



8-7616 



4-4944 



•0036 



■1156 



•0092 



•0 



e 2 i'm. 



1 



"18 



3 -68 

 7 13-48 



35 45-19 

 101 79-36 

 89 9610 

 94 90-90 

 70 71-41 

 46 48-25 

 30 28-53 

 15 14-94 



4 6-96 



5 2-88 



1 106 

 -34 

 -10 



o -oo 



•18 



7-9153 



3il50 



2-2977 



59008 



•5245 



•1058 



•0278 



•1049 



■0757 



■0002 



1-2523 



1-5605 



•0035 



•3400 



•0960 







2 



3 



4 



. 6 



7 



t 8 



9 



10 



11 



12 



13 ...... .. 



! 14 



15 



16 ., ... 



17 





Total ... 



500 



500-36* 



4- -36 





23-5000 



Thus gives i% 2 = 11*75 = ?;. say. 

 Then 



P = e- 



l +I 



+ 



+ ~ + 



+ 



5 



16 17 /' 



Substituting and working out we find 



P = -101 = 'l, say. 

 Or, in one out of every ten trials we should expect to differ 

 from the frequencies given by the curve by a set of devia- 

 tions as improbable or more improbable. Considering that we 

 should get a better fit of our observed and calculated fre- 

 quencies by (i.) reducing the moments, and (ii.) actually 



* Due to taking ordinates for areas and. fewer figures than were really 

 required in the calculations. 



