I need a 3.5 to get into the XY Degree. Also, Arguing about grades and grade points

1. When students tell me at the end of the semester, grades having been submitted, that they need a 3.5 grade-point average, say, to get into a certain degree program, and all I need do is change their grade from A- to A, or B+ to A-, my immediate thought is what were they doing in their other classes--not doing well, telling their instructors the same story, suddenly discovering they were not where they needed to be. Students who tell me they "always" get As, may well be just lucky, and ought to have gotten at least one A- or B+, or again did they tell all their instructors such stories. We always talk about the 4.0s at graduation, or sometimes the 4.0+s, but what I keep wondering is whether those persons are really good at something. They surely deserve their summa cum laude. I just don't know what I should take from such a grade point average. 

2. I received the following argument, from a student who received As on five projects and a B on a sixth, the projects to be weighted equally in the final grade. My point here is that such arithmetic is highly suspect, and there are arguments that are both reasonable and not at all inconsistent that come to a different conclusion.:

What this survey of the university regulations shows is 

A = 4.0 points

A– = 3.7 points and so on

This indicated that an A- is 3.7 out of 4 points, which is a 92.5. 

I received a 96! percent in your class (23/24), an A, not A-!

-----------------

The analysis is defective, since there is a mixing of percentages with grade points. If we look at the chart above, it is surely the case that you would get an A if you did 3.85 or better work (3.85 is halfway between 4 and 3.7), which is as little as 96.25% of the maximum grade, and if you got as little as 3.5 you would still get a A-, which is 87.5% of the maximum. You assume that an A means 100% but it could mean 96.5% in percentage terms. And a B might be as low as 2.85/4 which is 71.5% of the maximum. I have here assumed linearity, but in my experience excellent work is much much better than good work--you see that in your most distinguished professors who are much better than your quite good professors (who are very strong indeed). You really do not want to get to percentages when asking about excellence.

Actually, it is likely that your A's, were you graded in percentage terms, might well have been 95%.  Virtually no one does a perfect job. (Nor do we give A+ or say 110%, for spectacular.) So the letter grades tend to be a bit more generous than percentage grades, at this end of the scale.

If we were to go to the middle of the range of A's, that would be 3.925 and the B's would be 3, so the total of 5 As and 1 B would be 3+5x3.925, or 22.525 grade points, and dividing by 6 it is 3.777, well in the range of the A- (3.5 to 3.85). You might well have been in the upper tail or lower tail of the distribution, but that is not known here.