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Our school has a mandate that in any evaluation component (say quiz1, quiz2, etc.), the grades to be given are A, B, C and D to students. There is a further mandate that in any evaluation component (quiz1 for instance), the % of students receiving A should not be greater than 20% of the class and the % of students receiving A or B should not be greater than 60% of the class. [This implies that suppose all 100 students in my class had scored full points in both quizzes, all of them, unfortunately, necessarily have to receive a grade of C or D. (This has not happened thus far, thankfully!)]

We had two quizzes, quiz1 (15% weightage in GPA) and quiz2 (15% weightage in GPA). Technically, the mandate above applies to quiz1 separately and to quiz2 separately.

Can it be shown that if we do combine quiz1 and quiz2 into a single component QUIZ (say quiz1 was out of 50 points, and quiz2 out of 50 points, QUIZ = quiz1 + quiz2 out of 100 points) with QUIZ having weightage of 30% of the GPA, and apply quantiles to QUIZ to figure out the atmost 20% As and the atmost 60% As or Bs, that student grades would be better:

(a)on average, or

(b)even stronger, individually that no student is worse off in his final GPA for the course?

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I'm not defending the edict. However, if you give six quizzes of equal weight on which students get grades 1 through 5 (worst to best) with probabilities .1, .2, .4, and .2, respectively, and sum the six scores, then you'll likely have a reasonable spread of total scores to which final grades might be somewhat equitably assigned.

One simulated experiment with six such quizzes in a group of 100 students is summarized below:

set.seed(925)
t.5 = replicate(100, sum(sample(1:4, 6, rep=T, p=c(1,3,4,2))))
stripchart(t.5, meth="stack", ylim=c(0,5), pch=20)
table(t.5)
t.5
10 12 13 14 15 16 17 18 19 20 21 22  # total scores
 1  2 10  7 16 14 18 19  8  2  1  2  # numbers of students

enter image description here

The edict may be a way of suggesting not to construct quizzes on which all students get the same grade.

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  • $\begingroup$ Thank you. It is clear to me that combining will give a better spread of scores, can it be argued that students will be no worse off if they are assigned a grade (and hence a numerical gpa) based on the total sum instead of assigning individual grades to each of 6 components which are then combined in the usual way to obtain the final numerical gpa for the course? $\endgroup$ – Tryer Sep 25 '20 at 16:31
  • $\begingroup$ It would depend on what the 'usual' way of getting a numerical gpa is. $\endgroup$ – BruceET Sep 25 '20 at 16:34
  • $\begingroup$ What I meant by the 'usual' way was, suppose A=4, B=3, C=2, D=1. Suppose quiz1 (15%) student gets A, quiz2 (15%) student gets B, final exam (70% weightage) student gets A, then student's gpa = 0.15 x 4 + 0.15 x 3 + 0.7 x 4 = 3.85 $\endgroup$ – Tryer Sep 25 '20 at 17:17
  • $\begingroup$ If quiz scores and grade values are the same, then of course it can make no difference. // If you have a grading system in which no one can 'fail', then I wonder about its purpose? Merely to demoralize those who get D's, before 'passing' them on to get more D's? $\endgroup$ – BruceET Sep 25 '20 at 18:55

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