My original procedure for deciding letter grades led to some inconsistencies. Here is the revised procedure. The major grades were weighted 5, 3, 2, 4 for homework, lab, midterm and final. To judge the effect of the weighting on the course average, I computed three alternate grades. For the first, I reduced the weight of the homework by 2. For the second, I offweighted the midterm by 2 (which amounts to dropping it). For the third, I offweighted the final by 2. I computed a course average for all the students according to all these schemes. For each student I determined which average gave them the highest course average. This is the "nice average" mentioned above. The "worst component" is the component of your grade that was off-weighted to get your nice average. Thus, e. g. if your grade average is helped most by dropping the midterm, the third component of your grade (the midterm) is offweighted to obtain the nice average and the "worst component" is 3. Your worst component is not necessarily your lowest grade or the grade with your worst rank.
I assigned preliminary grades based on the ordinary average: >76=A, >73=A-, >69=B+, >63=B, >56=B-, >51=C+. Then I looked at the nice averages, to see whether anyone would be substantially helped by discounting their worst grade component. As it happened, the nice average didn't improve anyone's rank above that of someone with a higher letter grade. Thus I didn't modify anyone's grade in light of the nice averages.
NAME HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9 LAB1 LAB2 LAB3 MID FINAL Maximum score 30 40 30 30 40 10 30 50 40 10 10 10 30 53
final exam scores 41, 39, 34, 33, 33, 33, 32, 31, 29, 29, 28, 27, 27, 25, 24, 23, 23, 20, 10
30 33 22 27 35 7 30 49 35 1 1 12 9 4 10 1 2 3 omit 8.5 10 9 89.3333 91.7 19 33 91.1 91.7 63.3333 62.2642 2 1 2 4 4 79. 1 81.8 2 A 26 30 30 30 33 3 26 50 30 7 4 1 3 9 14 11 1 9 omit 9 9 9 86. 90. 8 41 87.9 90. 26.6667 77.3585 4 1 18 1 3 76.6 2 84.9 1 A 24 28 24 25 21 9 30 40 29 12 6 10 13 15 7 4 12 11 omit 6.5 10 10 76.6667 88.3 11 39 80.4 88.3 36.6667 73.5849 11 1 14 2 3 73.9 3 80.1 3 A- 24 25 25 27 20 8 23 42 35 10 8 6 10 17 9 14 11 4 omit 7.5 10 10 76.3333 91.7 15 33 80.4 91.7 50. 62.2642 10 1 4 6 3 73.3 4 77.2 4 A- 24 25 25 30 33 10 30 46 39 9 7 4 1 7 1 2 4 1 omit 7 7 10 87.3333 80. 12 31 88.1 80. 40. 58.4906 3 1 7 8 3 71.1 5 76.2 6 B+ 24 21 25 28 40 7 27 28 38 11 13 7 8 1 12 9 16 2 omit 9 8 8 79.3333 83.3 26 20 84. 83.3 86.6667 37.7358 9 1 1 18 4 71. 6 76.6 5 B+ 26 23 24 30 35 8 29 45 27 6 10 9 2 5 8 5 6 14 omit 9 8 8 82.3333 83.3 16 27 84.6 83.3 53.3333 50.9434 7 1 3 12 4 70.3 7 73.5 9 B+ 28 28 25 29 33 9 28 46 34 4 5 5 5 8 4 7 5 6 omit 7 7 8 86.6667 73.3 11 32 87.3 73.3 36.6667 60.3774 5 1 10 7 3 69.4 8 74.8 7 B+ 30 33 30 29 39 10 30 49 35 2 2 2 6 2 2 3 3 5 omit 8 7 9 95. 80. 12 23 94.8 80. 40. 43.3962 1 1 9 17 3 69.1 9 74. 8 B+ 22 22 Null 29 30 Null 28 24 27 13 11 17 4 10 17 6 17 13 omit 8.5 8.5 7 60.6667 80. 14 34 67.4 80. 46.6667 64.1509 15 1 5 3 3 66.2 10 69.5 11 B 26 32 26 29 36 2 26 44 30 8 3 3 7 3 16 12 9 10 omit 9 8 7 83.6667 80. 6 28 85.9 80. 20. 52.8302 6 1 19 11 3 65.8 11 73.4 10 B 28 24 24 27 35 10 27 45 32 5 9 11 11 6 3 10 7 8 omit 4 8.5 8.5 84. 70. 13 24 84.4 70. 43.3333 45.283 8 1 6 15 3 64.3 12 67.8 13 B 15 21 20 26 21 7 27 44 32 18 12 14 12 13 11 8 8 7 omit 7 8 8 71. 76.7 12 29 73.3 76.7 40. 54.717 12 1 8 9 3 64. 13 68. 12 B 16 20 24 23 30 9 Null 42 20 17 14 8 14 11 5 18 10 17 omit 8 8 9 61.3333 83.3 11 29 68.1 83.3 36.6667 54.717 13 1 11 10 3 63.1 14 67.5 14 B 21 18 16 21 20 6 21 38 26 14 15 16 15 16 13 16 13 15 omit 7.5 5 9 62.3333 71.7 8 33 63.3 71.7 26.6667 62.2642 16 1 17 5 3 59.6 15 65.1 15 B- 20 9 16 12 21 2 22 32 22 15 17 15 18 14 15 15 15 16 omit 8 10 9 52. 90. 11 23 53.3 90. 36.6667 43.3962 17 1 12 16 3 56. 16 59.2 16 B- 14 18 21 18 28 9 24 37 28 19 16 13 17 12 6 13 14 12 omit 7.5 7 9 65.6667 78.3 11 10 67.8 78.3 36.6667 18.8679 14 1 13 19 4 51.6 17 57.1 17 C+ 18 Null Null 21 Null Null Null Null Null 16 19 19 16 19 19 19 19 19 omit 6 Null Null 13. 20.7 10 27 15. 20.7 33.3333 50.9434 19 1 16 13 1 29.1 18 31.5 18 Q 28 Null Null Null Null Null 10 15 Null 3 18 18 19 18 18 17 18 18 omit Null Null Null 17.6667 1. 10 25 19.6 1. 33.3333 47.1698 18 1 15 14 1 25.5 19 26.4 19 Q