Saturday, February 12, 2011

Interpreting a grade distribution

Yesterday my genetics students wrote their second 'mini-midterm'.  This was a 25-minute quiz on the material we've covered in the last two weeks.  Everything went smoothly, the papers are graded, and the grades are posted along with the answer key.  But I don't know how to interpret the grade distribution.  Here's the histogram:

The quiz was open book, with five questions that were designed to require some thoughtful analysis but be very easy to mark (grading 38 papers took four of us about 30 minutes).  The questions weren't too difficult - 3 students earned perfect scores, and most had finished before the time was up.  They also weren't too easy - 12 students failed, and the mean score was only 15.8/25 (62%).

We expect grades on most tests to give a 'normal' distribution - the bell-shaped curve.  The curve may be skewed to the right if the exam was too easy, or to the left if it was too hard. A bimodal curve (with two humps) usually means that the students fall into two groups - those who have acquired some key skills and those who haven't.

But the grade distribution for this quiz looks flat to me, not really a curve at all.  It's flat all the way from 12% to 100%, with no more scores close to the mean than elsewhere.  I've never seen a grade distribution like this before and I don't know how it should be interpreted.  I can find technical descriptions of this shape in the context of a normal distribution (it's 'platykurtic') but I can't find any consideration of what this would imply about either students' abilities or the design of the test.

Maybe I'll ask my colleague in Curriculum Studies...

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