AVERAGE. If any number of unequal quantities are given, another quantity may be found of a Mean or intermediate magnitude, some of the given quantities being greater, and others less, than the one found, which is called the average, The exact relation is this: that the sum of the excesses of the greater above the A. is equal to the sum of_the defects of the less below it. If there are, say, 7 Vessels unequally filled with sand, and if we take handfuls from the greater, and add these to the less, until the sand is equally distributed, then any one of the equalized measures of sand is the A. of the 7 unequal measures. If the quantites of sand in the several vessels are stated in numbers. as 5, 10, 12, 8, 11, 14, 3 oz., the A. is found by adding together the numbers, and dividing by how many there are of them—viz., 7. The being 63, this, divided by 7, gives 9 oz. as the A. The system of averaging is a very important and time-saving one. By averages, the farmer calculates the value of his cropS; the grazier, the value of his cattle; and the forester, the value of his trees. Reflection, however, requires to be
exercised in striking averages; otherwise, serious errors may be committed. If a farmer, for instance, has three lots of cattle, the first of which he averages at f.:25 a head, the second at L'I5, and third at E9, it might be thought that the A. of the whole Sto• k made up of the three lots would be got by taking the mean of 1225, E15, and 1:9—viz., 25+15+9 But this would be correct only if there were an equal number of cattle in each of the lots. To get the real A. in case of the lots being nnequal, he must multiply the A. of each lot by the number of cattle in it, add the three products together, and divide by the whole number of cattle in all three lots taken together. If we suppose 9 head in the first lot, 20 in the second, and 15 in the third, the_A. iB 25 X9+15 X 20+9 x15_, 9+20+15