A Question for the Statisticians

Hypothetically speaking, let's say that there is a multi-section freshman-level math class. Furthermore, let's assume that during the semester all the instructors create and grade their own tests following fairly non-restrictive but meaningful guidelines; they all give the same number of tests on the same material weighted the same amount in the students' averages. At the end of the semester the final exam, written by the course coordinator, is common to all sections and graded communally, closely following a departmental rubric. The map from numerical scores to letter grades is the same for all sections.

Now let's imagine that a student in this course were to complain to me that the grades in Professor Newton's section are "way lower than the grades in all the other classes."

Supposing that I have access to all the final exam grades (raw scores), sorted by section but without students' names (each section is a column in a spreadsheet) and I also have access to the letter grade distributions for the sections (a staff member will tell me how many As, Bs, etc. were in each section), which statistical tests would I use to attempt to discern the validity of the student's claim? Specifically, I'm wondering if the letter grades in Newton's section are actually lower than the letter grades in other sections and whether any difference in course letter grades is consistent with the difference in performance on the final exam.