The Examination Curve

Abstract

IF the results of the examination of a mixed body of candidates be plotted out on the graphic method, they will be found, in accordance with a well-known law of statistics, to approximate to a curve having a more or less rapid gradient at either end, and a mid-region of gentler ascent. Fig. 1, for example, shows the results of an examination of 27 students in physical geography, the scale of marks running vertically from 10 to 90, the examinees being arranged horizontally at equal distances apart from the lowest to the highest. The larger the number of candidates the more flattened does the mid-region of the curve tend to become. Again, in any series of examinations, the mean results of which are plotted out, the more uniform the standard of difficulty of the papers set, the flatter is the mid region of mediocrity. Fig. 2 shows the mean results of ten separate examinations, of different students conducted by six examiners, in history, English literature, geography, physical geography, physics, botany, arithmetic, and Euclid. They are taken without special selection from the returns of class examinations in University College, Bristol. The standards were somewhat markedly different; in some the head, in others the tail, being excessive; hence the mid-region is not so flattened as it probably would have been had a larger series been taken. The results indicate, however, sufficiently well the general nature of the examination curve. The total range of marks being from 17˙5 per cent, to 84 per cent., 15 out of the 30 students fall within the mid-region of from 40 per cent. to 60 per cent.