CHAPTER XVIII. 



ON THE NATURE AND USE OF AN AVERAGE, AND ON THE 

 DIFFERENT KINDS OF AVERAGE 1 . 



1. WE have had such frequent occasion to refer to 

 averages, and to the kind of uniformity which they are apt 

 to display in contrast with individual objects or events, that 

 it will now be convenient to discuss somewhat more minutely 

 what are the different kinds of available average, and what 

 exactly are the functions they perform. 



1 There is much need of some good 

 account, accessible to the ordinary 

 English reader, of the nature and 

 properties of the principal kinds of 

 Mean. The common text-books of 

 Algebra suggest that there are only 

 three such, viz. the arithmetical, the 

 geometrical and the harmonical : 

 thus including two with which the 

 statistician has little or nothing to 

 do, and excluding two or more with 

 which he should have a great deal to 

 do. The best three references I can 

 give the reader are the following. 

 (1) The article Moyenne in the Dic- 

 tionnaire des Sciences Medicales, by 

 Dr Bertillon. This is written some 

 what from the Quetelet point of 

 view. (2) A paper by Feclmer in 



the Abliandlungen d. Math. 

 Classe d. Ron. Sachs. Gesellschaft d. 

 Wiss. 1878; pp. 176. This con 

 tains a very interesting discussion, 

 especially for the statistician, of a 

 number of different kinds of mean. 

 His account of the median is re 

 markably full and valuable. But 

 little mathematical knowledge is de 

 manded. (3) A paper by Mr F. Y. 

 Edgeworth in the Camb. Phil. Trans. 

 for 1885, entitled Observations and 

 Statistics. This demands some ma 

 thematical knowledge. Instead of 

 dealing, as such investigations gene 

 rally do, with only one Law of Error 

 and with only one kind of mean, it 

 covers a wide field of investigation. 



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