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This procedure is illustrative of the process in general, since when drop lowest = 0, the secondary recalculation is no longer necessary.
A category can only drop the lowest X items if all items under that category are equally weighted. Otherwise the drop lowest value is assumed to be 0.
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 = 1 100 / 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
- Sum the student's scaled weighted scores (x0y 0, x1 y 1 . . . xNy N)
- To determine the drop lowest order, sort the scaled scores
- If a drop lowest number is defined, drop that many items from the calculation
- Recalculate W based on the items that are still included
- Recalculate r based on the new W
- Recalculate Z based on the new r
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| 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 = 100
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:
| Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | W | r |
|---|---|---|---|---|---|---|---|
Scores | 95% | 80% | 87% | 79% | 100% | 100 | 0.01 |
xN | 0.95 |
...
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 |
In this case, of course, x i = y i, since r = 1. This means that Joe has been graded for all items in this category.
Therefore,
Z = 0.2375 + 0.2000 + 0.2175 + 0.1975 + 0.1000
Z = 0.9525
That is, his base grade for this category without including extra credit it 85.25% with an extra credit of 10%, so his category grade overall is 95.25%.
We can check this calculation easily, since in this particular case all items are equally weighted, so we can simply take the average of the four non-extra-credit items
average = (0.95 + 0.80 + 0.87 + 0.79) / 4 = 0.8525 = 85.25%
Calculating the projected course grade
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