for the percentages of services not metered should show some similarity in shape to the dotted line curve in Fig. 90, giving the yearly average of daily consumption.
When any curve fluctuates greatly, the general trend of the curve can be most easily determined if the method of moving averages is used. If data are plotted by months, a moving average is frequently made to include twelve months. As a succeeding month is included in the moving average, that calendar month of the preceding year is dropped out of the average so that the average always includes twelve months. The moving-average curve is a much smoother curve than a curve made from the monthly figures, and is accordingly more easily interpreted. The degree of smoothness of any moving-average curve depends chiefly on the number of points included in the moving average as compared with the number of points in one complete wave or cycle in the data curve, and the moving-average curve is most smooth if the moving average includes the same number of points as are usually found in one complete wave or cycle of the fluctuating curve.
Many curves plotted by weekly or monthly observations show a complete wave or cycle each year because of the effect of the seasons. With such a curve it is best to use for the moving average the number of points included in one year of the fluctuating curve. When, however, we study curves relating to financial conditions in any country, we find that there are complex cycles which involve several years. With such a complex curve considerable care must be used to determine the average length of one wave or cycle, so that the moving-average curve may be made as smooth as possible and most nearly represent the data being studied.
In Fig. 91 the data when plotted by years give such a complex curve that it is not easy to determine just how rapidly exports have increased. To show the effect of different numbers of points included in a moving average, curves were drawn with moving averages for three years, five years, and ten years. 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.
