Here's how the final course grade is calculated as a weighted average of the quiz and exam scores.
Each quiz is worth 15% of the course grade, and each exam is worth 35%, for a total of 100%. The easiest way to see how they get combined is to imagine a total of 100 points, of which 15 come from each quiz and 35 from each exam.
Each quiz has 20 questions on it. To make 20 quiz questions add up to 15 points, each quiz question has to be worth .75 (or 15/20 = 3/4) points, so you multiply each quiz total by .75.
Each exam has 40 questions on it. To make 40 exam questions add up to 35 points, each exam question has to be worth .875 (or 35/40 = 7/8) points, so you multiply each exam total by .875.
So your course total is
.75(quiz1) + .875(exam1) + .75(quiz2) + .875(exam2)
For example, scores of 14 on quiz 1, 31 on exam 2, 17 on quiz 2, and 33 on exam 4 would give
.75(14) + .875(31) + .75(17) + .875(33) = 79.25
A letter grade cutoff is the lowest score required to earn that letter grade. Sample letter grade cutoffs for each quiz and exam are listed below. (NOTE: These numbers are from another course and another semester and do NOT represent the actual cutoffs that will be determined from this course's score distributions. They may be the same in some cases, but that is only due to the similarity of the exam score distributions, which can vary by semester for each exam.) The final course letter grade categories come from applying the above weighting scheme to all the cutoffs. For instance, the course total required for a C from the cutoffs below is
.75(13) + .875(24) + .75(13) + .875(24) = 61.500
You earn the course letter grade corresponding to whatever category your course total falls into. The hypothetical student's score of 79.25 from the example above would earn a B, because it's higher than the B cutoff of 76.500 but not as high as the B+ cutoff of 81.500.
EXAMPLE NUMBERS ONLY - NOT THIS COURSE'S ACTUAL CUTOFFS
MINIMUM SCORES (CUTOFFS) FOR EACH LETTER GRADE QUIZ 1 EXAM 1 QUIZ 2 EXAM 2 COURSE TOTAL max: 20 40 20 40 100.000 Ê A 19 A 36 A 19 A 36 A 91.500 A A- 18 A- 34 A- 18 A- 34 A- 86.500 A- B+ 17 B+ 32 B+ 17 B+ 32 B+ 81.500 B+ B 16 B 30 B 16 B 30 B 76.500 B B- 15 B- 28 B- 15 B- 28 B- 71.500 B- C+ 14 C+ 26 C+ 14 C+ 26 C+ 66.500 C+ C 13 C 24 C 13 C 24 C 61.500 C C- 12 C- 22 C- 12 C- 22 C- 56.500 C- D+ 11 D+ 20 D+ 11 D+ 20 D+ 51.500 D+ D 10 D 18 D 10 D 18 D 46.500 D D- 9 D- 16 D- 9 D- 16 D- 41.500 D- F 0 F 0 F 0 F 0 F 0.000 FLetter grade cutoffs for each quiz and exam are determined from the score distribution of each semester's class on that quiz or exam. That's why this semester's cutoffs cannot be known before the quizzes and exams are actually given and the scores are analyzed. Though a given course's cutoff scores end up being fairly consistent from one semester to the next (due to consistent coverage of material and consistent class-level performance), different semesters may have lower or higher cutoffs than the example numbers shown above, for different exams. Lower cutoff scores generally result from more difficult exams. From one semester to another, the different cutoffs still reflect the same use of means and standard deviations, and the same criteria of fairness and generosity, as described below.
In general on my scale, the mean score divides the A and B grades from the C and D grades. Then roughly, the B grades are less than one standard deviation above the mean, while A grades are more than one standard deviation above the mean; likewise the C grades are less than one standard deviation below the mean, while D grades are more than one standard deviation below the mean, and F grades are more than two standard deviations below the mean. Pluses and minuses are added, as evenly spaced within each letter category as they can be. If those cutoffs end up being very borderline or ambiguous, I bend them in the direction of being generous, rather than making them stricter.
This scheme is always more generous than conventional percentage scoring (90% = A-, 80% = B-, 70% = C-, etc.), and in the unlikely event that a distribution was very high and this scale resulted in a lower score than the percentages would indicate, I'd give you the percentage-based higher score. In other words, you're guaranteed to get at least the score you'd expect from the conventional percentages, but my scale is usually more generous than that -- and it appropriately gives more of a boost to lower grades than to higher grades, since higher grades tend to already be nearly the highest they can get anyway.
I consider the common fix of a "curve" of adding a few points to every score (which mathematically speaking is actually a "line," anyway) to be arbitrary and ineffective, since the number of points added to the lower scores is limited by the number of points the instructor is willing to add to the highest score, when it's the lower scoring students who need the benefit of those points more. Surely the instructor adds points to allow more students to succeed at the low end, not because they think the highest scores deserve to be even higher. My scale helps more students and is the best I've come up with at being fair and generous with scoring standards. I hope you'll agree.