Prof. Edgeworth's Problems in Probabilities. 175 



A still less perfect verification is presented by a series of 



X. X. XX. XX. X. X 



85 14 50 100 225 



V. V. X. X. V. V. 



7 17'5 55 1225 225 



V. V. X. X. V. 



10 12'5 30 87"5 300 



eighty answers which I have obtained to the question : "How 

 many five-pound notes are equal in weight to a sovereign? " 

 The grouping of these estimates is represented in the first of 

 the annexed schemes * ; the grouping of two component 

 batches by the second and third scheme. It will be seen that 

 there is a general resemblance between the two parts and the 

 whole. The displacement of the Median seems not incon- 

 sistent with the hypothesis of a constant facility-curve. I thus 

 conclude, partly from a rough application of the formula which 

 I have cited from Laplace in the predecessor to this paper for 

 the error of the Median of any facility-curve f , partly by a 

 still rougher reasoning as to the divergency that might be 

 expected, if we were dealing with a genuine Probability- 

 curve. 



But it must be admitted that the upper extremity of the 

 curve defies law. The maximum of the first batch of 40 is 

 1500 ; the maximum of the second batch of 40 is 20,000 J. 

 These fluctuations are so violent that we could not expect to 

 determine their law of frequency without statistics more 

 copious than I have attained for examination marks. It 

 should be considered, however, that at examinations the 

 maximum and minimum are usually fixed, so that enormous 

 vibrations of the extremities are impossible. In so far as the 

 abnormal or incalculable element in the fluctuation of the 

 maximum or minimum may make itself felt, it should be held 

 that my estimates of the extent to which chance affects 

 examinations are underrated. 



These experiments in an intermediate case seem to warrant 

 our applying with caution the Theory of Errors to the more 

 specific experience which I shall now adduce. It consists of 



* Cf. p. 172. 



t Phil. Mag. October 1886, p. 375. 



\ The true figure is 6 ! 



