How your final grade is calculated
First, you have to know a little about statistics. I assume that the grades are drawn from a normal ("bell-curve") distribution. These distributions have an average (also called a mean) and a standard deviation (stdev), which measures how wide the distribution spreads out. A narrow distribution, one where students all got pretty much the same grade, has a small standard deviation; a wide distribution, one where there was a wide range of grades from very bad to very good, has a large standard deviation.
To compensate for the fact that the major exams, lab exams, final and project have different averages and standard deviations, I convert each score into a z-score. A z-score is the number of standard deviations your score was from the mean. Therefore:
- a z-score of 0 means you got class average
- a z-score of +1 means you got one standard deviation above class average
- a z-score of -1 means you got one standard deviation below class average
Z-scores are calculated using the following formula:
| Z-score = |
(your score - class average) |
| standard deviation |
Z-scores are then translated into your grades. You get an A if your z-score is 1 or above, a B if your z-score is between 0 and 1, and if your z-score is less than 0, you get a C or worse.
Here is the procedure step-by-step for the example below (2 midterms, a final and homework):
- I calculate the z-score for each exam.
- The two mid-term exam z-scores get multiplied by 0.15 (they are each weighted as 15% of your final grade) and added to your total z-score.
- I calculate the average and standard deviation for the homework total grade.
- I calculate your z-score for your homework grade, multiply it by 0.5 (it is weighted as 50% of your grade) and add it to your total z-score.
- I calculate the z-score for your final exam, multiply it by 0.2 (it is weighted as 20% of your final grade) and add it to your total z-score.
- Therefore, your total z-score corresponds to your final grade (z = 0 corresponds to the B/C border).
- I then sort all the students by total z-score and I evaluate any students near the borderline of each grade. Rarely, I move people up if I feel that their numerical grade does not reflect their work and contribution to the class.
Here it is for a randomly-chosen student:
These were the class-wide scores:
|
Exam 1 |
Exam 2 |
Final Exam |
Hwk Total |
| avg |
80.32 |
74.56 |
80.78 |
518.23 |
| stdev |
16.25 |
17.78 |
12.27 |
79.47 |
Here is the student's data:
|
Exam 1 |
Exam 2 |
Final Exam |
Hwk Total |
| Score |
87 |
85 |
84 |
581 |
| Z-score |
0.4111 |
0.5872 |
0.2624 |
0.7899 |
| weight |
0.15 |
0.15 |
0.20 |
0.50 |
| weighted z-score |
0.0617 |
0.0881 |
0.0525 |
0.3949 |
This student's total z-score = 0.0617 + 0.0881 + 0.0525 + 0.3949 = 0.5972 for a final grade of B.
Why do I do it this way?
It allows me to compensate for the fact that my exams have different averages and standard deviations.
Why is this important?
A score of 80 means something very different if the class average was 65 than if the class average was 85. Therefore, simply adding up total points is not appropriate unless the exam averages are very similar.