Since the distance between peaks on the curve making one cycle of fluctuation averages more nearly ten years than three years or five years, the ten-year curve more closely approximates a smooth curve line than either of the other two curves. As a matter of fact, the intervals between peaks change somewhat so that it is difficult to select any one number of years as the correct number for use in making up the moving average.

GRAPHIC METHODS

CURVE PLOTTING 99

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.