Grading on a Curve

I assign letter grades only at the end of the quarter. The letter grade is based on a cumulative score computed from a weighted average of homework, exam, and project scores. Consider the following data for a hypothetical student "X".

					Maximum		Score of
	Category		Weight		Possible Score		Student "X"
	Homework		15 %		250		207
	Midterm		30 %		110		88
	Project		25 %		90		75
	Final Exam		30 %		125		94

The weights express the relative importance of the evaluation (test, homework, etc.) in computing a cumulative score for the course. The maximum possible score varies from category to category for convenience of assigning grades on individual assignments. The maximum possible score does not really matter because the relative score, (your score)/(max possible score), is used to compute your cumulative grade.

Using the data from the table, the cumulative score of student "X" for this course is

0.15 × (207/250) + 0.30 × (88/110) + 0.25 × (75/90) + 0.30 × (94/125) = 0.798

So, student "X" gets a cumulative score of 80 % (rounded to two digits). Surely that is a "B", right?

The correct answer is, "It depends". When the final letter grade is based on a curve; a cumulative score means nothing all by itself . The letter grade corresponding to a cumulative score of 80 % depends on the cumulative scores of all other students in the class.

Below are histograms of two hypothetical cumulative score distributions for a class with 38 students. In both cases the dashed vertical line indicates the cumulative score of 0.798.