program get the average four sutdent that did five quizzes dropping the lowest q

Question

Explanation / Answer

Assume that a teacher has given a sequence of k > 0 quizzes and will allow each student to drop r of the quiz grades. Suppose that for j = 1, 2, 3, . . . , k a 1 particular student has earned on quiz j a score of mj points out of a possible nj points. For simplicity assume earned scores are integers, and possible points are positive integers. Let N be an upper bound for the nj . We will refer to the set of r grades that are dropped as the deletion set, and the set of k - r grades that are not dropped as the retained set. The goal is to identify the deletion set which will result in the student receiving the highest possible ?nal grade, the optimal deletion set. If the teacher is only basing the student’s ?nal grade on the student’s raw ? score, k mj , then ?nding the best grades to drop is a simple matter of j=1 ?nding the r smallest mj values and dropping them. For example, suppose that Alan has earned the quiz scores shown in Table 1. TABLE 1 : Quiz Score Possible Percentage Alan’s Quiz scores 1 2 3 2 6 24 8 12 40 25 50 60 If the teacher wants to drop two quiz scores, this student does the best by dropping quizzes 1 and 4 since those are the two with the smallest number of points assigned, leaving the student with an accumulated quiz total of 6 + 24 + 6 = 36, the largest possible sum of three scores. Notice that we dropped quiz 4, on which the student scored a higher percentage than on any other quiz. On the other hand, if the teacher is basing the student’s ?nal grade on the ratio of total points earned to the total points possible, then the problem of ?nding the best set of r scores to drop is far more interesting. What we need is a subset S ? K = {1, 2, 3, . . . , k} of k - r retained grades so that the ? j ratio ?j?S n is maximized. If all the quizzes are worth the same amount, j?S j that is, if all of the nj are equal, then this reduces to ?nding the r smallest mj values, just as it was in the above example. m

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.