SECT. 15.] Averages. 451 



able to start with something which existed, so to say, before 

 its variations ; but in many cases any starting point which 

 we can find is solely determined by the average. 



Suppose, for instance, we take a great number of ob 

 servations of the height of the barometer at a certain place, 

 at all times and seasons and in all weathers, we should 

 generally consider that the average of all these showed the 

 * true height for that place. What we really mean is that 

 the height at any moment is determined partly (and prin 

 cipally) by the height of the column of air above it, but partly 

 also by a number of other agencies such as local temperature, 

 moisture, wind, &c. These are sometimes more and some 

 times less effective, but their range being tolerably con 

 stant, and their distribution through this range being 

 tolerably symmetrical, the average of one large batch of 

 observations will be almost exactly the same as that of any 

 other. This constancy of the average is its truth. I am 

 quite aware that we find it difficult not to suppose that 

 there must be something more than this constancy, but we 

 are probably apt to be misled by the analogy of the other 

 class of cases, viz. those in which we are really aiming at 

 some sort of mark. 



15. As regards the practical methods available for 

 determining the various kinds of average there is very little 

 to be said ; as the arithmetical rules are simple and definite, 

 and involve nothing more than the inevitable drudgery 

 attendant upon dealing with long rows of figures. Perhaps 

 the most important contribution to this part of the subject is 

 furnished by Mr Gal ton s suggestion to substitute the median 

 for the mean, and thus to elicit the average with sufficient 

 accuracy by the mere act of grouping a number of objects 

 together. Thus he has given an ingenious suggestion for 

 obtaining the average height of a number of men without 



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