To make the process clearer, we will take a simple instance and imagine a community in which there were only three things purchased on a large scale by the citizens--wheat, bacon, and iron. We take for our year of reference, let us say, the year 1880, and we find that an ounce of gold would purchase one ton of wheat, half a ton of iron, and a quarter of a ton of bacon. But the amount spent on wheat was ten times the amount spent on bacon and twenty times the amount spent on iron. You add up the twenty tons of wheat, the half ton of iron and the half ton of bacon--half a ton of the latter because twice as much is spent on it as is spent on iron, and therefore though it is half the price of iron you must double the amount, because twice as much is bought. You get 21 tons. To buy this 21 tons of stuff 3 ounces of gold were needed. You divide the 21 tons by 3, and you get 7 tons of material on the average. Next, as you are taking this particular year for a “base” (or year of reference) you call the 7 “100,” so that you may compare in percentages the rise or fall of prices in other years. You then do exactly the same thing with these three staple commodities in another year--say 1890--and you find that your ounce of gold purchases no longer 7 tons of stuff, but 14 tons of stuff. Taking the year 1800 as your base number, you will see that the Index Number for 1890 is “50.” Then you do the same thing for the year 1920, and you find that with the same ounce of gold you can only purchase 3½ tons of stuff. 7 is to 3½ as 100 is to 200, so the Index Number for 1920 will be 200 as compared with the base year--or year of reference--which is 1880. You cannot use the Index Numbers without knowing what your base year is and what average prices were in that base year, but, having settled that, your Index Number is nothing more than a statement of _average prices_, or again, the average purchasing power of a fixed weight of gold in the various epochs you examine. In reality the calculating of an Index Number involves a great many more difficult points than these, and of course the number of commodities taken is very much more than three; but that is the method in its general outline, and if you go over it carefully I think you will not find it difficult to understand.[8]