A study of such a distribution would show not only that the average performance of the class has been raised, but also that those in the lower levels have, in considerable measure, been brought up; that is, that the teacher has been working with those who showed less ability, and not simply pushing ahead a few who had more than ordinary capacity. It would be possible to increase the average performance by working wholly with the upper half of the class while neglecting those who showed less ability. From a complete distribution, as has been given above, it has become evident that this has not been the method of the teacher. He has sought apparently to do everything that he could to improve the quality of work upon the part of all of the children in the class. It is very interesting to note, when such complete distributions are given, how the achievement of children in various classes overlaps. For example, the distribution of the number of examples on the Courtis tests, correctly finished in a given time by pupils in the seventh grades, makes it clear that there are children in the fifth grade who do better than many in the eighth. THE DISTRIBUTION OF THE NUMBER OF EXAMPLES CORRECTLY FINISHED IN THE GIVEN TIME BY PUPILS IN THE SEVERAL GRADES =================================================================== ADDITION | SUBTRACTION No. OF |----------------------+ No. OF |------------------------ EXAMPLES| GRADES | EXAMPLES | GRADES FINISHED| 5 | 6 | 7 | 8 | FINISHED | 5 | 6 | 7 | 8 --------+----+-----+-----+-----+----------+----+-----+-----+------- 0 | 12 | 15 | 5 | 4 | 0 | 6 | 2 | 2 | -- 1 | 26 | 23 | 14 | 9 | 1 | 5 | 6 | 2 | 1 2 | 27 | 31 | 8 | 6 | 2 | 7 | 8 | 1 | -- 3 | 31 | 27 | 27 | 9 | 3 | 13 | 21 | 3 | 1 4 | 25 | 28 | 19 | 16 | 4 | 21 | 18 | 13 | 2 5 | 16 | 23 | 16 | 15 | 5 | 26 | 30 | 12 | 7 6 | 15 | 22 | 12 | 12 | 6 | 17 | 27 | 15 | 9 7 | 1 | 11 | 8 | 9 | 7 | 15 | 27 | 18 | 9 8 | 3 | 4 | 6 | 11 | 8 | 15 | 20 | 12 | 12 9 | 1 | 2 | 3 | 8 | 9 | 10 | 13 | 9 | 12 10 | -- | -- | -- | 6 | 10 | 8 | 6 | 13 | 11 11 | -- | -- | 1 | -- | 11 | 6 | 2 | 3 | 12 12 | -- | -- | 1 | 2 | 12 | 3 | 1 | 7 | 9 13 | -- | -- | -- | -- | 13 | 2 | 2 | 3 | 5 14 | -- | -- | -- | -- | 14 | 1 | 1 | 3 | 7 15 | -- | -- | -- | 2 | 15 | -- | -- | 2 | 3 16 | -- | -- | -- | 1 | 16 | -- | -- | 1 | 2 17 | -- | -- | -- | -- | 17 | -- | 1 | -- | 1 18 | -- | -- | -- | -- | 18 | -- | -- | -- | 1 19 | -- | -- | -- | -- | 19 | -- | -- | -- | 4