The ranges for the plus/minus grades (such as B+ and B–) are 3.5 percentage points wide, but the ranges for the flat grades (such as B) are only 3 percentage points wide. Isn’t that weird?

Yes, considered by itself. But it reflects the fact that the grade points aren’t themselves evenly spaced: there’s a difference of 0.3 between some pairs of consecutive grade points (e.g., 3.0 and 3.3), but a difference of 0.4 between some others (e.g., 3.3 and 3.7). If the grade points were more evenly spaced (e.g., 3.00, 3.33, 3.67, etc.), then the mathematical technique used above (the one used to fill in table 6) would yield more equally sized percentage-point ranges for the letter grades.

Does that mean there’s something fishy about the fact that pluses and minuses are worth only 0.3 instead of 0.33?

No—the grades available in a grading system don’t need to be equally spaced along whatever numerical scales (e.g., grade points or percentages) they can be correlated with.

So why not just say that a B is anything between 83.33 and 86.67? Those numbers seem more intuitive, as thresholds, than 83.5 and 86.5.

Those numbers do seem more intuitive, but they can have some counter-intuitive consequences. To see this, suppose that, partway through the semester, a student is right in the middle of the B+ range, with an average of 88.33 (which is halfway between 86.67 and 89.99). She works hard to raise her average by 3.33 percentage points, to 91.66, which is right in the middle of the A– range (it’s halfway between 90.00 and 93.33). For her efforts, she is rewarded with an extra 0.4 grade points (3.7 grade points for an A– instead of 3.3 grade points for a B+). But now suppose this same student had been right in the middle of the B range, with an average of 85. Then her 3.3-percentage-point increase would have resulted in a final average of 88.33 (right in the middle of the B+ range, as we saw above). Then, her reward for her efforts would have been only 0.3 grade points (3.3 grade points for a B+ instead of 3 grade points for a B). It seems odd that the reward a student gets for raising her grade by a certain number of percentage points should depend, in this way, on where she started. My grading scale doesn’t allow this to happen, since it makes the distance from the middle to the B+ range to the middle of the A– range larger than the distance from the middle of the B range to the middle of the B+ range.

Here’s another way of looking at this issue. When thinking about pluses and minuses, it is natural to take ⅓ as the default plus/minus increment: grade points would be raised and lowered by this amount, we would use percentages like 83⅓ and 86⅔, and so on. When this default is deviated from, as with our plus/minus increment of 0.3, the percentages need to be adjusted accordingly. Under the default system, a student with an 85—in the middle of the B range—would need to raise her average by 1⅔ percentage points in order to get a B+. Her reward would be an extra ⅓ grade points. If her reward is going to be less than that, then the extra work she has to do should be less, too. Specifically, if her reward is going to be only 0.3 grade points, then the extra percentage points she needs should be 1⅔ times the ratio of 0.3 to ⅓. That ratio is 0.9, and 1⅔ times 0.9 is 1½. Hence my B+ threshold of 86½ rather than 86⅔. report this ad