...
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 = 100 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)
Z = sum of all the student's scaled scores for a given r
...
| Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | W |
|---|---|---|---|---|---|---|
Percent of Category | 25% | 25% | 25% | 25% | 10% | 100 |
W = 1001
r = 1
We can then look at Joe's actual percentage scores for each item and 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 | 0.25 | 0.10 |
p i | 0.95 | 0.80 | 0.87 | 0.79 | 1.00 |
x i | 0.2375 | 0.2000 | 0.2175 | 0.1975 | 0.1000 |
y i | 0.2375 | 0.2000 | 0.2175 | 0.1975 | 0.1000 |
...
Once the category scores have been calculated, a similar procedure is followed to determine if the the category weights must be redetermined (for example, if a given category has no graded items below it). Y
g j = category grade for each included category, as calculated from algorithm directly above
c j = category weight for each included category
h j = g j * c j
C = sum of all included category weights within a gradebook (the instructor's "best case" weights)
q where g j for that c j is not null
r = 1 / YC
Zf = (as above) the final sum of scaled scores for the category (this is the 'category score')
y = Zf * q
G v j = h j * r
% score = sum of all yh's above (y0h 0, y1 h 1 . . . yN)
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 | Y | q |
|---|---|---|---|---|---|---|---|---|---|---|
Joe (Weights) | 15% | 15% | 15% | 15% | 6% | 16% | 12% | 12% | 100% | |
Joe (Scores) | 95% | 75% | 80% | 85% | 92% | 87% | 100% | 95% | ||
Joe (yX) | 95% | 75% | 80% | 85% | 92% | 87% | 100% | 95% |
Melody (Weights) | 20% | 20% | 20% | - | 6% | - | 20% | 20% |
Melody (Scores) | 20% | 20% | 20% | - | 6% | - | 20% | 20% |
Francis (Weights) | 60% | - | - | - | 6% | 40% | - | - |
Francis (Scores) | 60% | - | - | - | 6% | 40% | - | - |
Roderick (Weights) | 100% | - | - | - | 6% | - | - | - |
Roderick (Scores) | 100% | - | - | - | 6% | - | - | - |
...
Student
...
Item 1
...
Item 2
...
Item 3
...
Item 4
...
Extra Credit Item
...
S
...
E
...
P
...
% score
...
Joe
...
20
...
20
...
20
...
excused
...
10
...
60
...
10
...
75
...
(60+10)/75 = 93.33%
...
Melody
...
20
...
20
...
20
...
20
...
10
...
80
...
10
...
100
...
h N)
So, if we were to calculate the course grade for Joe, assuming the following:
Category Name | Category Grade | Category Weight |
|---|---|---|
Category 1 | 0.9525 | 0.6000 |
Category 2 | 0.8725 | 0.4000 |
C = 1
r = 1
Variable | Category 1 | Category 2 |
|---|---|---|
g j | 0.9525 | 0.8725 |
c j | 0.6000 | 0.4000 |
h j | 0.5715 | 0.3490 |
v j | 0.5715 | 0.3490 |
% score = 0.5715 + 0.3490 = 0.9205 = 92.05%