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

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====== 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- | ===================
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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 we pass upward into the step .90 of the total distance (1.07 units), we shall arrive at a point .96 units (.90 x 1.07 = .96) above the lower limit of step 3, which we find from the table is 3.15.  Adding .96 to 3.15 gives 4.11 as the median point of this eighth grade distribution.

The median and the percentiles of any distribution of scores on the Hillegas scale may be determined in a manner similar to that illustrated above, if the scores are assigned to the individual papers according to the directions outlined above.