Grading on a curve is bastardized to mean various things to different people, but the common thread among must definitions is that it's an alternative to the strict 90-80-70 grading scale. Grading on a curve is the Holy Grail of university and high school students everywhere. Teachers who do not grade on a curve will be maligned behind their backs (as if they care) and whined at in class; teachers who grade on a curve will be treated with reverence by the students in the B-C range, who know they'd do worse otherwise.

The idea behind grading on a curve is that, rather than awarding a 100% to any student who gets a perfect score, the student with the highest score gets 100%, with all lower scores being tweaked accordingly. The point of this is that then the grades are not affected if the instructor has been teaching poorly, or if the test is more difficult (or easier) than anticipated by the instructor. It also serves to make school more competitive. There's more than one way to implement a curve-grading scheme, depending on the instructor's personal preference and the amount of effort they're willing to put into grading.

The simplest and, sadly, most common strategy is: find the minimum number of points missed (the score achieved by the best student) and subtract that number from the total possible points for the assignment in question. Then, apply the 90-80-70 scale to all students using the adjusted maximum score. So if a test had a possible score of 50, but nobody got better than a 43, all tests will be scored as if 43 was the maximum possible. A variant of this is to find the fifth best (or nth best) score instead of the best score. This will result in a few students getting over 100%, but compensates for the possibility of having one student who always gets 100% and the rest who get in the high 70s.

More ambitious grading schemes generally involve some sort of more advanced statistics. For example, an instructor may decide that 10% of the class should get As, 65% Bs, 20% Cs, and so on (See grade inflation if you're wondering why the instructor has decided ahead of time that 75% of the class will be above average). This is, effectively, partitioning the students' score data into arbitrarily defined quantiles corresponding to the various letter grades.
This method is not very common, because of its arbitrariness and rigidity.

The most sophisticated and flexible algorithm uses the statistical notion of a normal distribution. The mean and standard deviation of the data set (scores) is computed. Then, the instructor decides, arbitrarily, that the mean grade should be, for example, a 75%, and that a standard deviation will be worth 15% - so a student whose score is one std. dev. above the mean will get a 90%. This scheme, when based on a 75%/15% scale, will produce approximately the same number of As as Fs, and Bs as Ds. Despite its elegance and fairness, it is rarely used in schools (or the mean is set to something like 85%) because Fs are seen as really horrible and As, while nice, don't distinguish good students from great ones. Cry me a river, huh? That's grade inflation in action, I guess.

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