many can do seven, eight, and so on.  In penmanship we want to know how many children there are who write quality eight, or nine, or ten, or sixteen, or seventeen, as the case may be.  The work of the teacher can never be accomplished economically except as he gives more attention to those who are less proficient, and provides more and harder work for those who are capable, or else relieves the able members of the class from further work in the field.  It will be well, therefore, to prepare, for the sake of comparing grades within the same school or school system, or for the sake of preparing the work of a class at two different times during the year, a table which shows just how many children there are in the group who have reached each level of achievement.  Such tables for work in composition for a class at two different times, six months apart, appear as follows: 

DISTRIBUTION OF COMPOSITION SCORES FOR A SEVENTH GRADE

======================================
|  NUMBER OF CHILDREN
+-----------------------
|  NOVEMBER |  FEBRUARY
--------------+-----------+-----------
Rated at 0    |      0    |      0
1.83 |      1    |      1
2.60 |      6    |      4
3.69 |     12    |      6
4.74 |      8    |     11
5.85 |      3    |      4
6.75 |      1    |      3
7.72 |      1    |      2
8.38 |      0    |      1
9.37 |      0    |      0
======================================

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