JUNE, 1951
311
A SLIDE RULE FOR AVERAGING GRADES OR EXPERIMENTAL DATA DWIGHT PAY MOWERY, JR. Trinity College, Hartford, Connecticut
INORDER to save time and increase accuracy in averaging student grades, a circular slide rule of special design was found to he very satisfactory. The rule consists of two concentric movable discs and a hairline marker of transparent plastic. The larger of the discs carries a perfectly regular scale completely around it, numbered from 0 to 100. The smaller disc, which can be rotated upon the larger, carries a series of scales of I/d, etc., down to '/20 of the angular lengths, length of the fixed scale. These scales are marked 2, 3, 4, etc., up to 20, and are used for averaging 2,3,4, etc., up to 20 two-digit grades or instrument readings. For example, if 35, 60, and 72 are to be averaged, the hairline is set simultaneously a t the 100 mark on the outside disc and the zero point of the scale marked 3 (since three figures are to he averaged). Then the hairline is moved to 35 on the No. 3 scale and held in position by pinching the end of the marker and the edge of the large disc. The smaller disc is then rotated until the zero point of the No. 3 scale is again under the hairline and the marker moved to 60 on this scale. The end of the marker and edge of the large disc are again pinched and the inside disc rotated to that the zero point of the No. 3 scale is again under the hairline and the hairline moved to 72 on this same scale. The average of the three numbers can now readily he determined on the outside scale as 55.6. It will he seen that actually one is merely stepping off and thereby adding on the large outside scale, a third of 35, a third of 60, and a third of 72, and the sum is the average of the three. The division by three is brought about automatically, since the angular length of the No. 3 scale is exactly one-third of the length of the large outside scale. If four numbers are to be averaged, the No. 4 scale is used, and up to twenty figures can be averaged by choice of the appropriate scale. In averaging large numbers of figures, the slight errors unavoidable in each individual setting tend to cancel out so that the h a 1 average is not greatly in error. In most cases the average calculated by the rule is within 0.2 of a unit of the true average. If more than twenty figures are to he averaged, as for example, in determining a class average, the total number of figures can be divided into halves, thirds, or some other fraction and the average of each fraction deter-
Av-aee
Calcvleto.
mined, and then these figures averaged. It is obvious that if thirty-seven grades are to be averaged, two groups, one containing 18, and the other 19, could be averaged separately, and then these two figures averaged equally on the No. 2 scale, without introducing an appreciable error. For weighted averages, for example, of three figures, one weighted 3, the second 2, and the third 1, the No. 6 scale is selected and the first figure is stepped off three times, the second, twice, and the third, once. The mle can he used to average experimental data or instrument readings or any other figures which differ only in the last two digits. This slide rule has been used by the author for the past year for averaging student grades, and has been estimated to reduce the time involved to less than ouehalf, while decreasing considerably the chance of making serious and embarrassing mistakes. It makes unnecessary the copying of grades from grade books for addition'or division, the only figure which need be written down being the final average.
