Further information on grading curves

One of my most frequently asked questions is how do I drop the lowest hourly exam. The answer is a bit complicated, but the explanation is fairly informative. Students' worry about this issue can be justified by the following example. Suppose I post a curve after exam 1 where a 31 out of 35 is a low A while a 31 out of 35 is declared to be a high B on the test 2 curve. Suppose also that you get a 31 on both exams. According to the curves, your performance on test 1 is slightly better than on test 2, and I can register your scores accordingly so that I drop your lowest score after normalizing it to the curve. Here is how I do that. Each test's scores can be averaged to give an average (mean). In the field of descriptive statistics, the mean may be the number you are most familiar with. But the distribution of grades also yields another descriptive statistic, the standard deviation, which indicates how spread out the distribution is. By subtracting the mean from your score and dividing by the standard deviation, a score called the z-score is calculated. This gives your position in the distribution just like a percentile is calculated from the standardized scores in college and graduate (professional) school admissions. This may seem like a lot of calculating, but the spread sheet programs available on desktop computers makes it quite easy for me to drop your lowest z-score. Also, it is noteworthy that I use your scores, not your grades. That means, for instance, that a high B is a whole lot better than a low B, and, correspondingly, one high B and two high C's would very likely average to something in the B range. Most students who take all 3 tests will benefit when the lowest of the 3 is dropped, so keep this in mind!

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revised 3/7/02