Education ∪ Math ∪ Technology

Educators make mistakes when grading. It happens. Sometimes we mark a student’s work lower than we should, compared to their peers, and sometimes we mark it higher than we should. The question is, what effect does this have on a student’s overall mark?

Here are some sample grades. The sample column is the original grade, the low column is a mark 1 lower than the sample, the high column is a mark 1 higher than the sample.

 Grades Sample Low High Quizzes 5 4 6 6 5 7 7 6 8 5 4 6 6 5 7 7 6 8 5 4 6 6 5 7 5 4 6 6 5 7 average 5.8 4.8 6.8 Homework 5 3 5 5 3 5 3 1 5 3 1 5 1 1 3 1 1 3 3 1 5 5 3 5 3 1 3 average 3.222222 1.666667 4.333333 Tests 40 35 45 45 40 50 35 30 40 40 35 45 30 25 35 average 38 33 43 Overall Grade 70.1 55.9 82.5

The overall grade was calculated here by finding the averages of the three categories (quizzes, homework, and tests – standard categories in many classes) with quizzes worth 20%, homework worth 20%, and tests worth 60% of the overall grade. These aren’t particularly unusual grades. Note, however, how wide the possible error is in the final grade, which could potentially actually range from 55.9% to 82.5%, which is a 26.6%, or a HUGE amount in any grading system.

Of course, teachers aren’t likely to mark everything low, or everything high. One could make an assumption that both of these cases are equally likely, and then instead of using the likely minimum mark, and the likely maximum mark, we could try and aim for 2 standard deviations from the mean of the possible grading outcomes. In other words, what’s a likely range?