It must be remembered that cumulative curves always refer to some definite length of time and that they must always begin at the beginning of the period for which the summation is made. Cumulative curves do not extend outward indefinitely, but start over again at zero with each succeeding period of time. Thus, cumulative curves plotted by months or weeks on a long sheet of paper, for a series of years, would be seen in the shape of saw teeth, with the highest point at the end of each fiscal year and then a drop to zero again at the beginning of the next fiscal year. The saw-tooth shape makes it feasible, and sometimes desirable for easy comparison, to plot cumulative curves for several successive periods of time in the same space, as the two cumulative curves in Fig. 135 are plotted.

The progressive average shown by means of the dotted lines in Fig. 135 is obtained by averaging each month the values for all the points

154 GRAPHIC METHODS

given on each curve since the beginning of each fiscal year. For November the average includes two months, for December three months, for January four months, etc. The progressive averages in this chart mean comparatively little and can be of almost no assistance to the manager studying them. The daily averages and the progressjve averages would have been much more striking if the averages for the two years had been plotted horizontally instead of as superimposed curves. A moving average could then be shown continuously so that the average would always take in twelve months without having to start over again at the beginning of the second fiscal year. The information in Fig. 135 would have been more simple in appearance and more quickly apprehended if it had been given on two separate sheets of paper, the daily average curve and the suggested movingaverage curve being shown for two years horizontally on one sheet, the cumulative curves being shown on a different sheet with the two years superimposed on the same scale, as in Fig. 135.