error in that different years might be compared without the reader's noticing that he was making an error. In starting a new curve on a five-year card the curve should be started in the middle of the card if the first year plotted happens to fall in the middle of a half-decade. The half-decade arrangement should be carefully followed even though it does not leave a portion of a card unfilled.
The fine-line curve running through Fig. 215 represents a twelve-*months moving average of the points on the heavy curve. If the executive wishes to know the general trend of his costs, he refers at once to this fine line and sees what the cost has been for the last twelve months for which costs are known. In making up this moving average (as explained in Chapter VI), one month is dropped from the addition and another month is included in the addition, so that the twelve months added are always the most recent months for which figures are available. Note in Fig. 215 the degree of accuracy used in recording the figures for the curves. Costs are known quite accurately in this case and are recorded here to one one-hundredth of a cent. The moving-average line shown above is a much simpler line than the curve line, for the reason that the violent fluctuations in the heavy curve are largely eliminated by the method of moving averages. The general rule for smoothing a curve is that the number of points included in the moving average should be the number ordinarily found in one complete cycle or wave on the curve. This principle also was more fully discussed in Chapter VI. In Fig. 215 the length of the wave is approximately one year. It is accordingly good practice to have twelve points included here in making up the moving average, so as to give as smooth a curve as possible. If there had been a complete wave or cycle every six months instead of once a year, it would have been desirable to use six points in the moving average, rather than twelve points. The practice in many offices is to use the last twelve months in making up a moving average, though it frequently occurs that a smoother curve would be obtained if some other number of months were used.
As will be seen by reference to Fig. 91, points for a moving-average curve are usually plotted in the middle of the horizontal space covered by those points included in the moving average. In executive-control curves such as are seen here, it seems desirable to make an exception to the general rule and plot the last point on the moving-average curve so that it falls on the same vertical co-ordinate line as the last point included in the average. If the moving-average curve were made as
