...
| 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 = 1
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:
...
average = (0.95 + 0.80 + 0.87 + 0.79) / 4 = 0.8525 = 85.25%
Calculating the projected course grade
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).
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) where g j for that c j is not null
r = 1 / C
v j = h j * r
% score = sum of all h's above (h 0, h 1 . . . 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%
Melody's Case
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 = 1.0334We can then repeat this calculation for some arbitrary "Category 2" scores for Joe:
| Item 2.1 | Item 2.2 | Item 2.3 |
|---|---|---|---|
Percent of Category | 40.00% | 30.00% | 30.00% |
W = 1
r = 1
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 2.1 | Item 2.2 | Item 2.3 |
|---|---|---|---|
w i | 0.40 | 0.30 | 0.30 |
p i | 0.85 | 0.88 | 0.87 |
x i | 0.3400 | 0.2640 | 0.2610 |
y i | 0.3400 | 0.2640 | 0.2610 |
Therefore,
Z 2 = 0.3400 + 0.2640 + 0.2610
Z 2 = 0.8650
Calculating the projected course grade
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).
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) where g j for that c j is not null
r = 1 / C
v j = h j * r
% score = sum of all h's above (h 0, h 1 . . . 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 | 0.8650 | 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 | 0.3460 |
v j | 0.5715 | 0.3460 |
% score = 0.5715 + 0.3460 = 0.9175 = 91.75%
Melody's Case
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 |
|---|---|---|---|---|---|
Percent of Category | 25.00% | 25.00% | 25.00% | 10.00% |
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 1 = 0.2967 + 0.3100 + 0.3267 + 0.1000
Z 1 = 1.0334
Melody's "Category 2" Item Weights:
| Item 2.1 | Item 2.2 | Item 2.3 |
|---|---|---|---|
Percent of Category | 30.00% | 30.00% |
W = 0.6
r = 1.666666 (repeating)
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 2.1 | Item 2.2 | Item 2.3 |
|---|---|---|---|
w i | 0.33 | 0.33 | |
p i | 0.87 | 0.91 | |
x i | 0.2871 | 0.3003 | |
y i | 0.4785 | 0.5005 |
Therefore,
Z 2 = 0.4785 + 0.5005
Z 2 = 0.9790
Melody's projected course grade
Category Name | Category Grade | Category Weight |
|---|---|---|
Category 1 | 1.0334 | 0.6000 |
Category 2 | 0.9790 | 0.4000 |
C = 1
r = 1
Variable | Category 1 | Category 2 |
|---|---|---|
g j | 1.0334 | 0.9790 |
c j | 0.6000 | 0.4000 |
h j | 0.62004 | 0.3916 |
v j | 0.62004 | 0.3916 |
% score = 0.62004 + 0.3916 = 1.0116 = 101.16%
Summary of example scores
Student | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | Z 1 | Item 2.1 | Item 2.2 | Item 2.3 | Z 2 | % score |
|---|---|---|---|---|---|---|---|---|---|---|---|
Joe | 0.95 | 0.80 | 0.87 | 0.79 | 1.00 | 0.9525 | 16% | 12% | 12% | 0.8725 | (0.9525*0.6) + (0.8725*0.4) = 92.05% |
Melody | 0.89 | 0.93 | 0.98 | 1.00 | 1.0334 | - | 0.87 | 0.91 | 0.8811 | (1.0334*0.6) + (0.9790*0.4) = 101.16% | |
Francis | 0.87 | - | - | - | 1.00 | tba | 0.76 | - | - | tba | tba |
Roderick | 1.00 | - | - | - | 1.00 | tba | - | - | - | tba | tba |