Elliott C. Back: In Aere Aedificare

When taking a course graded by a large staff, you might wonder how fair the grading is. After all, no two people grade the same way, and the criteria can be interpreted differently. Some graders are tough for syntax problems in programs, while others are more interested in style. It’s impossible to know whether they’re objective or not without data.

Fortunately, a friend who works for a University happened to have the data lying around for an introductory CS course. There were 15 graders, and 437 data points, for an average of 29 assignments and tests per grader. The course, he said, enrolls about 150 students every semester, and is the gateway into acceptance into the CS major. Without further ado, allow me to present a graph of the average grade given per grader:

The average mean grade given was 78.9; the standard deviation of grades given by each grader was 5.4, indicating that the majority of grades fell on average into a 73 - 84 point spread. The data is probably complicated by the performance of students and would require complicated multi-factor analysis, of which I know nothing, to sort it out.

N	Mean	SE Mean	StDev
15	78.87	1.40	5.43

Minimum	Q1	Median	Q3	Maximum
68.50	74.50	80.80	82.90	87.10

It’s mildly reassuring that the data seems to be left-skew, indicating that graders tend away from the normal distribution in favor of slightly more lenient grading. However, the spread between the averages of the worst and best graders is a whopping 18.6 points. Should a student have to bet his grade in a critical course on which grader happens to get him? No. As long as the assignment of graders is essentially random–the case in this course–which grader does which student shouldn’t affect their grades significantly if the graders follow a normal distribution–almost the case here.

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