448 Averages. [CHAR xvin. 



The reasons for employing this latter kind of average in 

 preference to any of the others will be indicated in the fol 

 lowing chapter. At present we are concerned only with the 

 general logical nature of an average, and it is therefore 1 

 sufficient to point out that any such intermediate value will 

 answer the purpose of giving a rough and summary indica 

 tion of the degree of closeness of approximation which our 

 various measures display to each other and to their common 

 average. If we were to speak respectively of the first and 

 the second average/ we might say that the former of these 

 assigns a rough single substitute for the plurality of original 

 values, whilst the latter gives a similar rough estimate of the 

 degree of their departure from the former. 



12. So far we have only been considering the general 

 nature of an average, and the principal kinds of average 

 practically in use. We must now enquire more particularly 

 what are the principal purposes for which averages are em 

 ployed. 



In this respect the first thing we have to do is to raise 

 doubts in the reader s mind on a subject on which he 

 perhaps has not hitherto felt the slightest doubt. Every 

 one is more or lest familiar with the practice of appealing to 

 an average in order to secure accuracy. But distinctly what 

 we begin by doing is to sacrifice accuracy ; for in place of 

 the plurality of actual results we get a single result which 



here, J^ . Galloway commonly !** ^.* the ex P ressio Mean 



V n Error, (widely in use in its more 



speaks of the Mean Square of the natural signification,) as the equiva- 



Errors to represent ?? . I shall to ^f&amp;gt;^.M.S. 



n The technical term Fluctuation 



adhere to the former usage and re- is applied by Mr F. Y. Edgeworth to 



present it briefly by E.M. S. Still ., . 2Se 2 



more unfortunate (to my thinking) ~vT 



is the employment, by Mr Merriman 



