Prof. Edge worth's Problems in Probabilities. 173 



1. designates the first sixteen estimates which I received. The 

 second column contains the average of each batch, expressed 

 in pounds above nine stone. The third column gives the 

 average of the sixteen errors measured without regard to sign 

 from the average of each batch, and multiplied by the con- 

 stant 1*25/ = a / -nearly) for the sake of comparison w T ith 



the entries in the fourth column, each of which is the Mean 

 of similarly reckoned errors, in the Gaussian sense of Mean 

 Error : that is, the square root of the sum of squares of errors 

 divided by the number thereof less by one, that is here 15. 



Order of 



entry. 



Average. 



Average error 

 X 1-25. 



Mean error. 



I. 



II. 



III. 



IV. 



V. 

 VI. 



24-5 



23 



22-5 



22 

 29 

 29 



8-2 

 7-6 

 8 

 10 

 6-6 

 9 



8-1 



7-8 



86 



9-8 



6 



9-6 



Means ... 



25 



8-2 



8, 



It will be observed that these estimates obey not only a law, 

 but the law of error ; according to which the Mean Error 



ought to be equal to the Average Error x \ /— . For further 



verification of this incident I may refer to the scheme on 

 page 172, where it appears that the probable error, as deduced 

 from the distribution of the observations, is 5. Now, according 

 to the Tables compiled for the Error-function, the number of 

 observations outside a distance on either side from the centre 

 of three times the probable error ought to be 4'3 per cent. 

 That is exactly what occurs. It is true that the average and 

 mean error do not perfectly fit the probable error. But the 

 imperfection is hardly greater than might be expected in 

 dealing with a number of observations so limited as 96. Nor 

 would I contend for a perfect fulfilment of the law of error — 

 more perfect than in the case of human statures and other 



