12.10 Ten graduate students take identical comprehensive examinations in their major field. The grading procedure is that each professor ranks each student’s paper in relation to all others taking the examination.

Suppose that four professors give the following ranks, where 1 indicates the best paper and 10 the worst.

Student Professor 1 2 3 4 5 6 7 8 9 10 1 5 3 8 9 2 7 6 1 4 10 2 7 4 6 2 3 9 8 5 1 10 3 3 5 7 6 4 10 8 2 1 9 4 4 5 7 8 3 9 6 1 2 10

(a) Is there evidence of agreement among the four professors?

(b) Give an overall estimate of the relative performance of each student.

(c) Will it be difficult to decide which students should receive a passing grade?