178 Prof. EdgewortiYs Problems in Probabilities. 



Designation. 



Number of Marks 



on which the 



Computation is 



based. 



Mean 

 Discrepancy 

 per cent, of 

 mean mark. 



High School, Geometry and History . . . 



Cambridge Honours in Classics, Trans- 

 lation, History, Composition (mixed) 



India Civil Service, Latin Prose Corn- 



160 



480 



28 



480 



150 



800 



15 



18 

 20 

 21 



25 



28 



Oxford Honours in Literse Huma- 



Cambridge Honours in Classics, Com- 

 position (alone) 



English Composition 





These data are adapted to certain problems which are of 

 practical interest. 



I. The first problem is, What is the probability that 

 any particular candidate who has come out successful at an 

 examination would have been successful (or vice versa) 

 if the candidate's work and that of his competitors had 

 been appraised by a different though equally competent 

 examiner (or examiners) ? This general problem may be 

 variously subdivided. First (A) success may be defined by 

 the attainment of* a predetermined number of marks, a fixed 

 Honour Line. Or (B) the number of prizes, say n, may be 

 predetermined ; and the first n candidates, without respect to 

 the absolute number of their marks, may obtain prizes. Other 

 distinctions turn on the presence or absence of an attribute 

 which is particularly favourable to the calculation of proba- 

 bility: namely, a certain plurality which renders applicable 

 the laws of large numbers ; the attribute in virtue of which 

 the movement of multitudinous atoms is more tractable than 

 the problem of three bodies. We may inquire whether a 

 candidate would be displaced, if (x) the mark assigned to 

 each paper in each subject had been what may be called the 

 true mark — namely the mean of the marks given by an inde- 

 finite number of equally competent examiners ; or (#) , if the 

 marks in each subject had been given by a single examiner 

 (or a few) different from the one (or two) who acted on the 

 given occasion. Again (y) the number of competing candi- 

 dates may be large, or (y) not so. Lastly (z) there may be 



