Calculating Weighted GPAs

Like most schools, ours uses an online system for entering and tracking grades (Aspen). I really like being able to verify and track grades. Some teachers are really slow, but with other teachers, I know my son's grade before he does. Considering the importance of grades and GPA in high school, this is much better than his middle school's mysterious rubrics and work that disappeared into black hole portfolios never to be seen unless you set up an appointment with each teacher.

The reason for this post started when I couldn't verify a quarter grade in one subject. (I know that many teachers hate the system and that you have to set up weird rules to have it do what you want.) My calculations showed that he should have gotten a 93 instead of a 92 for a grade in one quarter. Then, I found out that fixing that number would have no effect on his semester (half-year) grade or his weighted GPA. What was going on?

Our high school calculates a weighted GPA to use for class rank. Regular college prep courses have a weight of 3, honors classes have a weight of 3.4, and AP classes have a weight of 3.7. (The AP arms race this causes is a separate issue.) Course grades (by semester - half year) are multiplied by the weight and a credit score; 1 for a full year course and .5 for a half year course. The score is normalized using the sum of the credits. If you get a 100 in a full-year honors class, this would give you a weighted and normalized score of 100 * 3.4 = 340. The weighted GPA is summed for all courses and then divided by the sum of the credits. This means that weighted GPAs for students typically end up between 250 and 325.

The first problem is that the semester grade for each class is rounded to the nearest whole number before it multiplied by the course weight. OK, but the problem is that they round grades at every step of the way. First, each assignment and test is rounded to the nearest whole number (that's fine), and then they are combined together into groups called things like formative and summative. The formative might be 30 percent of your grade and the summative might be 70 percent of your grade. Some teachers have five or more categories. Each one of these categories is calculated and the grade is rounded off to the nearest whole number. Then, these whole numbers are combined to form a quarter grade, which of course is rounded to the nearest whole number. This is done again for the second quarter. After the second quarter, students are given a midterm test. To form the semester (half-year) grade, they count each quarter as 40 percent and the midterm as 20 percent. (It's common for midterm grades to be far lower than either quarter grade, but that's another issue.) This semester grade is also rounded to the nearest whole number before multiplying it by the weight for the course. When the online system displays the weighted GPA, it's displayed using four decimal digits. The roudings are supposed to balance out? No. They are throwing away significant digits and hoping that statistics will recover accuracy. Interestingly, my son's grades have far more rounding downs than ups. Each assignment might be accurate to plus or minus one point, but there is no justification for rounding numbers at every other step of the process. That's why it doesn't matter whether my son got a 92 or 93 on his quarter grade.

Actually, it gets worse. Our high school just emailed us a list of the top ten seniors for this year. (My son is still a junior.). I guess many high schools set this ranking in stone after the first half of the senior year because they have to send something out on the transcrips to colleges. So how do they calculate this final GPA? They do something different at the half-year (semester) point. They take the grade for each course, multiply it by the course weight (3, 3.4, or 3.7), but then multiply it by the full year credit for he course. This gives the semester grade a weight equal to a full year course. I raised this issue with a guidance counselor who said that this is how they've done it for all of the 25+ years she has been there.

I'm sure they use all of those decimal digits of accuracy on the printout to rank kids. They really need to define a proper matematical bound on their accuracy and not just throw away accuracy by repeated rounding.