174 Prof. Edgeworth's Problems in Probabilities. 



natural groups*. Indeed lam not concerned to show that the 

 law of error is fulfilled ; except so far as this incident may 

 afford some guarantee of greater stability. It is on this 

 account only, if at all, that I am concerned with another 

 striking incident, namely that the Mean of all the estimates t, 

 the apparent weight, 9 st. + 25 lb., coincides with the real 

 weight, which is exactly, or oscillates about, 10 st. 11 lb. 



A less perfect, but still I think sufficient, verification of our 

 axiom is afforded by another series of 96 estimates which I 

 obtained by asking the additional question : " What is my 



XIX. XXXII. XXVI. XIX. 



7'5 9 10 



XIII. XVI. XI. VIII. 



VI. XV. XVI. XI. 



height"? The grouping of the series is as before exhibited 

 by the first two rows of figures in the annexed scheme. 

 The correspondence of the parts with the whole and with 

 each other is shown by the third and fourth rows, referring 

 respectively to the first and second batches of forty- eight 

 estimates. The average of the thirty-five errors in defect — 

 measured from the average of the ninety-six observations, 

 namely 8*6 — is T73. The average of the first eighteen 

 errors in defect is 1'55. The average of the remaining 

 seventeen errors in defect is 1*9. Again, the average of 

 the sixty-one errors in excess is *98. The average of the 

 first thirty-one of those errors is 1 ; the average of the 

 remaining thirty is *9G. 



As in the case of the weights, the apparent land true measures 

 coincide. But there does not exist that guarantee of stability 

 which may be afforded by conformity to a Probability-curve. 

 That hypothesis is negatived by the protuberance of the lower 

 limb which has just now been evidenced. It may be added 

 that, whereas the lower quartile is distant from the Median 

 by less than 1*5, there occur (in so small a set) three observa- 

 tions distant respectively from the Median 5, 7, 8. This 

 occasional darting out of the lower limb is unfavourable to 

 that steadiness in the average of small batches which we 

 noticed in the case of the weights. The Medians of compo- 

 nent batches are sufficiently steady §. 



* The aggregation of observations at round numbers is one of the 

 vitiating causes in both cases. 



t The Arithmetic Mean and Median coincide. 



\ Taking as the apparent weight 8f , intermediate between the average 

 which is 85 nearly and the median which is 9 nearly. 



§ For further details see the companion paper. 



