Page:Popular Science Monthly Volume 66.djvu/374

370 to a discussion of college grades. The literature is very scanty. I can only refer to two papers, both of which are slight.

Grades are usually assigned on a scale of 100, some institutions, as Harvard and Columbia, reporting only the five groups into which the men are divided. The starting point in all grades is the fact that the written papers or the results of the term's work can be arranged more or less accurately in the order of merit. The assignment of quantitative grades to a qualitative series or its division into groups is usually done in an arbitrary manner, and, so far as I am aware, no attempt has hitherto been made to assign probable errors. It is obvious that our grades should be standardized. Our colleges are in the position of a grocer who should let each of his clerks give to customers without weighing and without knowledge of market prices what he believed to be a dollar's worth of tea.

The simplest method of assigning grades is to arrange a hundred papers as nearly as may be in the order of merit and to give the poorest paper the grade 1, the next poorest the grade 2, and so on, until the best paper receives the grade 100. The 100 cases would not be exactly representative of the entire group with which we are concerned; but if we had 100,000 cases, the error from this source in giving the poorest 1,000 the grade of 1, etc. would be entirely negligible. It is possible to calculate how likely it is that in a random group of 100 cases we should find two, three or more men to whom the lowest or any other grade should be assigned. Each instructor forms a rough estimate of the group of students with which he is concerned, and can with a probable error that might be determined assign its place in the series to each case.

If men are arranged in this way in the order of merit and each is assigned his position in the series from 1 to 100, the differences between them will not be equal. If a hundred men are placed in a row according to height, the line passing along the tops of their heads will not be a straight line. The men in the middle of the row will differ but little from one another, and the differences will become continually greater towards the ends. Fig. 1 (page 366) shows the approximate distribution in stature of 1,052 English women, measured for Professor Karl Pearson. Their average height was about 5 feet 2 inches; 18.3 per cent, of the whole number were between 62 and 63 inches, and one half of them were within about 1 inches of the average, the probable error. The ordinates or vertical lines are