27 December 2013
Exam scores and the final exam solutions are available on ICON. Also, the normalized scores for all exams, homeworks, and quizzes are new columns, with a weighted overall score as well (each of these new columns is scaled from 0.00 to 100.0). The final grade curve computation is finished, visible in one of the columns (the last estimated GPA 12/24) on ICON.
Grading / Curve Algorithm
The Syllabus states that final grades have three categories, exams, homeworks and quizzes:
- Exams count 50% of the final grade
- Quizzes count 20% of the final grade
- Homeworks count 30% of the final grade
The algorithm to construct a curve will first do a kind of normalization of each of the three categories. In each category, each student will have a point total (such as the sum of all quiz scores for the quiz category). We will normalize by finding the highest total over all students, for each category. Such a highest total will be equated to 100% for the purposes of normalizing. Then, each student/category total will be scaled to a number in the range 0.0--100.0 (so that the highest score equates to 100.0). After this normalization step, each of the three categories will have a number in the range 0.0--100.0. At this point, the percentages above can be applied: 50%, 20%, and 30% for the respective categories. Multiplying each category score by the percentage, then summing over the three categories, will result in a number in the range 0.0--100.0 for every student (but, it could be that the maximum is not 100.0 because some students are not the best in every category). Finally, after one more normalization, the summed and scaled numbers are scaled to 0.0--100.0.
The result of the normalizing, scaling and summing above does not automatically give us a curve for grading. For that, we need additional steps to try and match the suggested College of Liberal Arts and Sciences grade distribution. This is done heuristically by calculating mean, standard deviation, and then binning the totals to approximate the suggested distribution. The goal is to find natural separations of point totals so that students who are close in point totals get the same grade, yet have sufficient separation between the totals for different grades so that minor mistakes (either in student performance or evaluation) do not change the grades. As a double-check on grades, we look back at homeworks, quizzes and exams to confirm that the heuristic is sensible.