h the 1 composition rated at 0 and count up through the 9
rated at 1 and the 32 rated at 2 in the above distribution, we shall
have counted 42. In order to count out 77 cases, then, it will be
necessary to count out 35 of the 39 cases rated at 3.

Now we know (if the instructions given above have been followed) that
the compositions rated at 3 were so rated by virtue of the fact that the
judges considered them nearer in quality to the sample valued at 3.69
than to any other sample on the scale. We should expect, then, to find
that some of those rated at 3 were only slightly nearer to the sample
valued at 3.69 than they were to the sample valued at 2.60, while others
were only slightly nearer to 3.69 than they were to 4.74. Just how the
39 compositions rated on 3 were distributed between these two extremes
we do not know, but the best single assumption to make is that they are
distributed at equal intervals on step 3. Assuming, then, that the
papers rated at 3 are distributed evenly over that step, we shall have
covered .90 (35/39 = .897 = .90) of the entire step 3 by the time we
have counted out 35 of the 39 papers falling on this step.

It now becomes necessary to examine more closely just what are the
limits of step 3. It is evident from what has been said above that 3.69
is the middle step 3 and that step 3 extends downward from 3.69 halfway
to 2.60, and upward from 3.69 halfway to 4.74. The table given below
shows the range and the length of each step in the Hillegas Scale for
English Composition.

THE HILLEGAS SCALE FOR ENGLISH COMPOSITION

======================================================
STEP No.|VALUE or SAMPLE|RANGE OF STEP |LENGTH OF STEP
--------+---------------+--------------+--------------
0. . . .| 0 | 0- .91[32] | .91
1. . . .| 1.83 | .92-2.21 | 1.30
2. . . .| 2.60 |2.22-3.14 | .93
3. . . .| 3.69 |3.15-4.21 | 1.07
4. . . .| 4.74 |4.22-5.29 | 1.08
5. . . .| 5.85 |5.30-6.30 | 1.00
6. . . .| 6.75 |6.30-7.23 | .93
7. . . .| 7.72 |7.24-8.05 | .81
8. . . .| 8.38 |8.05-8.87 | .82
9. . . .| 9.37 |8.88- |
======================================================

From the above table we find that step 3 has a length of 1.07 units. If
we count out 35 of the 39 papers, or, in other words, if w