438 Averages. [CHAP. XVIIL 



and that it is therefore appropriate only in definite circum 

 stances. The reason why it affords a safe and accurate 

 intermediate value for the actual divergent values, is that 

 for many of the ordinary purposes of life, such as purchase 

 and sale, we come to exactly the same result, whether we 

 take account of those existent divergences, or suppose all 

 the objects equated to their average. What the grazier 

 must be understood to mean, if he wishes to be accurate, by 

 saying that the average price of his sheep is 50 shillings, is, 

 that so far as that flock is concerned (and so far as he is 

 concerned), it comes to exactly the same thing, whether they 

 are each sold at different prices, or are all sold at the aver 

 age price. Accordingly, w r hen he compares his sales of one 

 year with those of another ; when he says that last year the 

 sheep averaged 48 shillings against the 50 of this year ; the 

 employment of this representative or average value is a great 

 simplification, and is perfectly accurate for the purpose in 

 question. 



3. (2) Now consider this case. A certain population is 

 found to have doubled itself in 100 years : can we talk of an 

 average increase here of 1 per cent, annually ? The cir 

 cumstances are not quite the same as in the former case, but 

 the analogy is sufficiently close for our purpose. The answer 

 is decidedly, No. If 100 articles of any kind are sold for 100, 

 we say that the average price is 1. By this we mean that 

 the total amount is the same whether the entire lot are sold 

 for 100, or whether we split the lot up into individuals 

 and sell each of these for 1. The average price here is a 

 convenient fictitious substitute, which can be applied for 

 each individual without altering the aggregate total. If 

 therefore the question be, Will a supposed increase of 1 p. c. 

 in each of the 100 years be equivalent to a total increase to 

 double the original amount ? we are proposing a closely 1 



