 Ben Eggleston

Also new for the school year, are three additional calculator tools, the GPA Calculator, the Final Grade Calculator, and the Monthly Expense Calculator to help you stay on top of your educational costs and manage your monthly expenses.

# Instructions:

Type in the grades you’ve received, along with the weights they’ll have in the determination of your overall average.

Then, if you want, fill in one or both of the fields embedded in the questions marked ‘ OPTIONAL:’. After you press ‘Compute’, the results will show your average so far, as well as the answer(s) to any question(s) whose embedded fields you filled in.

Every grade you enter must be a non-negative number, and every percentage you enter must be a positive number.

- What is the plus and minus grading scale and how does it affect my GPA?

This is a question I'm often asked by students, so I have written a short paper to demonstrate how I determine minimum percentages when using the plus and minus grading scale. # The Problem

In the Fall 2008 semester, the College of Liberal Arts and Sciences added grades with pluses and minuses (A–, B+, etc.) to its list of available grades. (Such grades had been available in some schools at KU previously, but not in the College.) Here are the web pages stating the KU and CLAS grade lists:
http://www.registrar.ku.edu/~registr/transcript/overview.shtml http://www.collegesas.ku.edu/policies/GPA.shtml

When the only grades were A, B, C, D, and F, it was pretty easy to come up with a final grade calculator, and it was easy for me to show students how to calculate grade percentage. For example, I usually used the following grading scale:

Table 1:
A90
B80
C70
D60
F

With the introduction of pluses and minuses, minimum percentages need to be determined for a much longer list of grades, as shown in table 2. (For now I’ll assume the possibility of A+, even though it is not an available grade at KU, and then I’ll adjust for its absence at the end.)

Table 2:
A+?
A?
A-?
B+?
B?
B-?
C+?
C?
C-?
D+?
D?
D-?
F

# My Solution

If you think of the new grading scale as dividing each of the old grades’ ranges into three smaller ranges (e.g., the A range gets divided into ranges for A+, A, and A–), it seems logical to think that the minimum percentage for an A– under my new grading scale should be the same as the minimum percentage for an A under my old grading scale, that the minimum percentage for a B– under my new grading scale should be the same as the minimum percentage for a B under my old grading scale, and so on. So I can partially fill in my table as follows:

Table 3:
A+?
A?
A-90
B+?
B?
B-80
C+?
C?
C-70
D+?
D?
D-60
F

Now, I’d like for the other minimum percentages to be based on KU’s grade-point conversion scale:

Table 4:
A+?
A4
A-3.7
B+3.3
B3
B-2.7
C+2.3
C2
C-1.7
D+1.3
D1
D-0.7
F

Notice, though, that there is a structural mismatch between tables 1–3 and table 4. The former were concerned with minimum values, and the latter is concerned with middle values (e.g., 3 grade points goes with the middle of the B range—it has nothing to do with the bottom of the B range). So, to use KU’s grade-point conversion scale to figure out my new percentage-based grading scale, I need to pay attention to middle percentages, not minimum percentages. My old grading scale had 95 in the middle of the A range, 85 in the middle of the B range, and so on. I’ll keep these as the middle percentages in my new grading scale:

Table 5:
A+
A95
A-?
B+?
B85
B-?
C+?
C75
C-?
D+?
D65
D-?
F

Now, to fill in the other percentages using KU’s grade-point conversion scale, I’ll assume that the relative spacing of the grades on KU’s grade-point conversion scale should dictate the relative spacing of the grades’ middle percentages on my grading scale. I’ll start with the B+. Since a B+ is worth 3.3 grade points, and 3.3 is 30 percent of the way from a B (3.0) to an A (4.0), I want to know what number is 30 percent of the way from an 85 to a 95. That number, of course, is 88. So, that should be the middle percentage for a B+. By similar reasoning (working with 3.7 grade points for an A–), the middle percentage for an A– should be a 92. Filling in the other values analogously, I have the following:

Table 6:
A+98
A95
A-92
B+88
B85
B-82
C+78
C75
C-72
D+68
D65
D-62
F

With these middle values determined, all I need to do to figure out the corresponding ranges is to figure out the midpoints that lie between consecutive numbers:

Table 7:
A+9896.5
A9593.5
A-9290
B+8886.5
B8583.5
B-8280
C+7876.5
C7573.5
C-7270
D+6866.5
D6563.5
D-62
F

Now, there are just a couple of further decisions I have to make. First, what should the threshold between D– and F be? For consistency with my old grading scale and for consistency between D– and the other minus grades under my new grading scale, I’ll make it 60.

Second, should a student whose percentage is equal to a threshold percentage get the letter grade just above it, or just below? For reasons of charity, I prefer to award the letter grade just above it. So, these thresholds are actually the minimum percentages for the grades just above them. That means that I can completely fill in the “minimum percentage” table I started with, but couldn’t get very far with at the time (table 3):

Table 8:
A+96.5
A93.5
A-90
B+86.5
B83.5
B-80
C+76.5
C73.5
C-70
D+66.5
D63.5
D-60
F

So that’s the way I would assign letter grades, under a complete plus/minus system. KU’s grading system, however, maxes out at A; there is no A+. So I need to make an adjustment. One way of handling this is to enlarge the intervals associated with each of the eleven remaining passing grades (A down to D–). But that would violate a lot of the constraints I’ve operated with so far, as well as being a mess.

A second option is to proportionally enlarge the intervals associated with A and A–, so that 90 remains the minimum value for A–, with 95 being the new minimum value for A. This, however, would make the unavailability of the A+ grade result in a disproportionately high percentage required in order to get an A. I think that would make A’s harder to get than they should be. A third option, my preferred one, is just to absorb the values associated with A+ into the range for A. So, the minimum value for an A would remain 93.5, and anything above that (up to 100, or higher, for that matter) would still be an A:

Table 9:
A93.5
A-90
B+86.5
B83.5
B-80
C+76.5
C73.5
C-70
D+66.5
D63.5
D-60
F

So those are the minimum percentages I use. In most courses, I grade individual assignments on a scale of 0 to 100, and then at the end of the semester I use Blackboard or Excel to compute each student’s final average to the nearest hundredth of a percentage point. So, in practice, my grading scale is as follows:

Table 10:
A93.50 and above
A-90.00–93.49
B+86.50–89.99
B83.50–86.49
B-80.00–83.49
C+76.50–79.99
C73.50–76.49
C-70.00–73.49
D+66.50–69.99
D63.50–66.49
D-60.00–63.49
F59.99 and below

1. 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.

2. 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.

3. 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.