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This is an essential strategy in order to cleanly project grades throughout the quarter/semester/trimester, so the instructor can see how well his or her students are doing based on the items that have been graded, even before all the scores are in.
Drop Lowest
When calculating a category score with the number of drop lowest items > 0, it is necessary to first calculate the re-weighted scores for all items for that student based on which items are graded and not excused, then to remove the lowest values and recalculate the weights again.
This procedure is illustrative of the process in general, since when drop lowest = 0, the secondary recalculation is no longer necessary.
W = sum of all included item weights within a category (the instructor's "best case" weights)
r = 1 / W
p = percentage score for a given item (points earned / points possible)
x = p * r (scaled score for a given item)
Z = sum of all the student's scaled scores for a given r
- Sum the student's scaled scores (x0, x1 . . . xN)
- 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
| Note |
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A category can only drop the lowest X items if all items under that category are equally weighted. |
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).
Y = sum of all included category weights within a gradebook (the instructor's "best case" weights)
q = 1 / Y
Zf = (as above) the final sum of scaled scores for the category (this is the 'category score')
y = Zf * q
G = sum of all y's above (y0, y1 . . . yN)