444 Averages. [CHAP. xvm. 



Another example, taken from natural phenomena, may 

 be found in the heights of the barometer as taken at the 

 same hour on successive days. So far as 4857 of these may 

 be regarded as furnishing a sufficiently stable basis of ex 

 perience, it certainly seems that the resulting curve of fre 

 quency is asymmetrical. The mean height here was found 

 to be 29-98: the median was 30 01 : the most frequent 

 height was 30 05. The close approximation amongst these 

 is an indication that the asymmetry is slight 1 . 



8. It must be clearly understood that the average, of 

 whatever kind it may be, from the mere fact of its being a 

 single substitute for an actual plurality of observed values, 

 must let slip a considerable amount of information. In fact 

 it is only introduced for economy. It may entail no loss 

 when used for some one assigned purpose, as in our ex 

 ample about the sheep ; but for purposes in general it 

 cannot possibly take the place of the original diversity, by 

 yielding all the information which they contained. If all 

 this is to be retained we must resort to some other method. 

 Practically we generally do one of two things: either (1) we 

 put all the figures down in statistical tables, or (2) we ap 

 peal to a diagram. This last plan is convenient when the 

 data are very numerous, or when we wish to display or to 

 discover the nature of the law of facility under which they 

 range. 



The mere assignment of an average lets drop nearly all 

 of this, confining itself to the indication of an intermediate 



1 A diagram illustrative of this was noted. That is, 29 9 includes 

 number of results was given in all values between 29 900 and 29-999. 

 Nature (Sept. 1, 1887). In calculat- Thus the value most frequently en- 

 ing, as above, the different means, I tered in my tables was 30-0, but on 

 may remark that the original results the usual principles of interpolation 

 were given to three decimal places ; this is reckoned as 30-05. 

 but, in classing them, only one place 



