First let's understand the three scenarios we'll work with.
- A percentage scale that recognizes zero as the lowest possible grade.
- A percentage scale that recognizes 50 as the lowest possible grade.
- A 4-point scale that recognizes zero as the lowest possible grade.
We'll now look at 3 students who received three grades that are averaged accordingly.
Student A: Percentage: 80, 70 and 0; 4-point: 3, 2, 0
Student B: Percentage: 90, 80 and 0; 4-point: 4, 3, 0
Student C: Percentage: 60, 80 and 0; 4-point: 1, 3, 0
Under Scenario 1
Student A: (80+70+0)/3 = 50
Student B: (90+80+0)/3 = 57
Student C: (60+80+0)/3 = 47
Under Scenario 2
Student A: (80+70+50)/3 = 67
Student B: (90+80+50)/3 = 73
Student C: (60+80+50)/3 = 63
Under Scenario 3
Student A: (3+2+0)/3 = 1.7 or 67
Student B: (4+3+0)/3 = 2.3 or 73
Student C: (1+3+0)/3 = 1.3 or 63
You can see that scenario 2 and 3 align well as they give similar results to all three students. Scenario 1 gives the most punitive results. Similar results can be obtained using a variety of different scores. While, scenario 2 and 3 may not provide exactly the same scores for the three students, they will closely align. This validates the practice of using 50 rather than zero as the base. If we want to align the percentage scale with the 4-point scale, we need to address the disproportionate failure range by setting 50 as the floor for failure. Using 50 as the floor allows us to continue using the familiar percentage scale for grading, while at the same time ensuring the fairness that the 4-point scale offers.
