268 MEMORIES of MY LIFE
cision to the meaning of " class-place." The familiar phrases of top of his class, near the top, half-way down it, and the like, express a great deal, but they express much more if used in connection with the size of the class. A useful way of reducing classes of all sizes to a common one is as follows. The names of the individuals are entered in the order of their classplaces in a long column, beginning with the highest. The names are separated by lines which resemble the rungs of a ladder, and will here be called rungs for distinction. The interval between the lowest and highest rungs is divided along the sides of the ladder into equal parts to form a scale, usually one of ioo parts. I n this the lowest rung stands at o and the highest at i oo . Such divisions are called centiles. If the divisions are not in hundredths, but otherwise as tenths, eighths, or quarters, they are still called by words ending in "-ile," as decile, octile, and quartile. The marks corresponding to the class-places at each centile, decile, octile, or quartile, are independent of the size of the class, except in that small degree to which all statistical deductions are liable when derived from different samples of the same store of material.
The diagram opposite explains the process. For reasons of space it is adapted here to a class of only twelve individuals, but it is applicable equally well to classes however large, and the larger the better.
The method of centiles affords a convenient and compact way of comparing the amounts of specified faculties in different individals. All this is an old tale now, but I had to take a great deal of trouble before it was clearly thought out and well tested.