AVERAGE is a quantity intermediate to a number of other quantities, so that the sum total of its excesses above those which are less, is equal to the sum total of its defects from those which are greater. Or, the average is the quantity which will remain in each of a number of lots, if we take from one and add to another till all have the same ; it being supposed that there is no fund to increase any one lot, except what comes from the reduction of others. Thus, 7 is the average of 2, 3, 4, 6, 13, and 14; for the sum of the excesses of 7 above 2, 3, 4, and 6—that is, the sum of 5, 4, 3, and 1—is 13 ; and the sum of the defects of 7 from 13 and 14 that is, the sum of 6 and 7—is also 13. Similarly, the average of 6 and 7 is 64 To find the average of any number of quantities, add them all toyether, an divide by the number of rantittes. Thus, in the preceding question, add together 2, 3, 4, 6, 13, and 14, which gives 42 ; divide by the number of them, or 6, which gives 7, the average.
It must be remembered that the average of a set of averages is not the average of the whole, unless there are equal numbers of quantities in each set averaged. This will be seen by taking the average of the whole, without having recourse to the partial averages. For instance, if 10 men have on the average 1001., and 50 other
men have on the average 3001., the aver age sum possessed by each individual is not the average of 100/. and 3001. ; for the 10 men have among them 10001., and the 50 men have among them 15,0001., being 16,000/. in all. This, divided into 60 parts, gives 266/. 13s. 4d. to each. A neglect of this remark might lead to erro neous estimates; as, for instance, if a harvest were called good because an average bushel of its corn was better than that of another, without taking into account the number of bushels of the two.
The average quantity is a valuable common-sense test of the goodness or badness of any particular lot, but only when there is a perfect similarity of cir cumstances in the things compared. For instance, no one would think of calling a tree well grown because it gave more timber than the average of all trees; but if any particular tree, say an oak, yielded more timber than the average of all oaks of the same age, it would be called good, because if every oak gave the same, the quantity of oak timber would be greater than it is. It must also be remembered that the value of the average, in the information which it gives, diminishes as the quantities averaged vary more from each other.