CHAPTER XIX. 



THE THEORY OF THE AVERAGE AS A MEANS OF 

 APPROXIMATION TO THE TRUTH. 



1. IN the last chapter we were occupied with the Average 

 mainly under its qualitative rather than its quantitative 

 aspect. That is, we discussed its general nature, its principal 

 varieties, and the main uses to which it could be put in 

 ordinary life or in reasoning processes which did not claim to 

 be very exact. It is now time to enter more minutely into 

 the specific question of the employment of the average in 

 the way peculiarly appropriate to Probability. That is, we 

 must be supposed to have a certain number of measure 

 ments, in the widest sense of that term, placed before us, 

 and to be prepared to answer such questions as ; Why do we 

 take their average ? With what degree of confidence ? 

 Must we in all cases take the average, and, if so, one always 

 of the same kind ? 



The subject upon which we are thus entering is one 

 which, under its most general theoretic treatment, has per 

 haps given rise to more profound investigation, to a greater 

 variety of opinion, and in consequence to a more extensive 

 history and literature, than any other single problem within 

 the range of mathematics 1 . But, in spite of this, the main 



1 Mr Mansfield Merriman pub- necticut Acad.) a list of 408 writings 

 lished in 1877 (Trans, of the Con- on tne subject of Least Squares. 



v. 30 



