...
w i = item weight within a category
W = sum of all included item weights within a category excluding extra credit items (the instructor's "best case" weights)
r = 1 / W
p i = percentage score for a given item (points earned / points possible)
x i = p * w (weighted score for a given item: x 0, x 1 . . . x N)
y i = w * r (scaled weighted score for a given item: y 0, y 1 . . . y N), though with extra credit items r is fixed at 1.00
Z = sum of all the student's scaled scores for a given r
...
So, if you remember from the table above and copied below, Melody had two items unscored or excused, one in each category. The result was that the overall course grade percentages for her graded items increased in value, as shown in this table. *Note that these percentages are not category weights, but course grade percentages, that is, the product of an item weight and a category weight: *
Student | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | Item 2.1 | Item 2.2 | Item 2.3 |
|---|---|---|---|---|---|---|---|---|
Joe | 15% | 15% | 15% | 15% | 6% | 16% | 12% | 12% |
Melody | 20% | 20% | 20% | - | 6% | - | 20% | 20% |
Francis | 60% | - | - | - | 6% | 40% | - | - |
Roderick | 100% | - | - | - | 6% | - | - | - |
If we assign some arbitrary scores for these items, we can perform the same calculations we did above for Joe, but taking into account the excused/missing items.
Melody's "Category 1" Item weights:
| Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | W |
|---|---|---|---|---|---|---|
Percent of Category | 25.00% | 25.00% | 25.00% | 10.00% | 100 |
W = 0.75
r = 1.3333333 (repeating)
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item |
|---|---|---|---|---|---|
w i | 0.25 | 0.25 | 0.25 | 0.10 | |
p i | 0.89 | 0.93 | 0.98 | 1.00 | |
x i | 0.2225 | 0.2325 | 0.2450 | 0.1000 | |
y i | 0.2967 | 0.3100 | 0.3267 | 0.1000 |
Therefore,
Z = 0.2967 + 0.3100 + 0.3267 + 0.1000
Z = 1.0334