The heavy smooth curve was drawn finally by using the points which represent the averages of the decades and then sketching in, free hand, a line which gives a smooth curve and removes the waves found in the ten-year moving-average curve. Notice that the heavy smooth curve is so drawn through the ten-year curve as to give approximately equal areas on either side of the smooth curve between that curve and the curve for the ten-year moving average. The curve for the ten-year moving average evidently does not give a fair interpretation of yearly data, because the ten-year average curve shows a peak in the year 1886 while the data as plotted by years show a valley for that year. The peak in the ten-year moving-average curve in 1886 was caused by the number of years included in the moving average not being a true representation of the length of one full cycle. The length of the cycle changes from time to time, so that no one selected cycle length is satisfactory for the whole curve. The heavy curve sketched in by hand is the fairest approximation to show the trend of the fluctuating curve as a whole.
In Fig. 91 the points on any smoothed curve are plotted midway horizontally in the range of years included in each moving average. It is on this account that the smoothed curves, though all plotted from the same data, do not seem to end at the same year at the right-hand side of the chart. Though it is good practice to plot smoothed curves in this manner with each point midway in the horizontal range of the points included in any moving average, there are times when it is not desirable to have the point on the moving-average curve fall behind the latest point on the data curve. For operating records in industrial work, the moving-average curve is convenient to show an average for the preceding twelve months or for any other length of time immediately preceding. With such curves it is usually best to have the last point of the moving-average curve plotted on the same vertical co-ordinate line as the last point of the data curve.
Index numbers are used very commonly in the study of facts relating to the prices of commodities over a long period of time. When making comparisons by index numbers, conditions are selected which as nearly as possible represent the normal or typical conditions for the subject under consideration. The figures for other dates are then compared with the figures representing the normal conditions, by working on a percentage basis so that the figures for the normal conditions are taken as unity or 100 per cent. Figures for the conditions to be
