Know Your Grade: Single Assignments
In each of my classes I use a weighted average to compute student grades. Assignments are divided up into categories like exams, homework, and labs. Each category is assigned a weight as a percent of the total grade with each assignment within that category having equal weight. I’ve noticed that students often struggle understanding their grades when dealing with these kinds of weighted averages. In this post we’ll look at how one can understand how a single assignment will impact their final grade in such a grading system.
Single Assignment Weight
Let’s say that exams are worth 35% of your grade and that there are a total of 7 exams. Each individual exam is worth 5% of your total grade because each exam is an equally weighted so the 35% category weight is equally distributed amongst the exams. What would the weight of a homework assignment be if homework was 25% of your grade and you had 8 homework assignments? In this case we take 25/8 to get 3.125% per homework assignment. In general, the weight of an assignment is equal to the weight of the assignment’s category divided by the number of assignments in the category.
One source of confusion arises when assignments within a category are graded differently. Let’s go back to 7 exams with an overall exam weight of 35% and assume that one exam has a total of 45 points where another has 75. The 75 point exam carries no more weight than the 45 point exam when it comes to your final grade. A grade of a B on both of them has the same overall impact on your grade. However, a point on the 45 point exam is technically worth more than a point on the 75 point exam. If each exam accounts for 5% of your grade, then we can further distribute that 5% across each point. This means that a point on the 45 point exam is worth 1/9, or 5/45, of a percentage point on your final grade where a point on the 75 point exam is worth 1/15, or 5/75, of a percentage point. I wouldn’t get too hung up on this distinction though. If you’re looking at the big picture, then look at the overall assignment grade as a percentage. The important observation here is that the total points on the assignment do not necessarily reflect the impact of the assignment on your final grade in the course.
Single Assignment Impact
Once an assignment is scored, you can combine the actual grade earned with the assignment weight to assess the impact that assignment will have on your overall grade. We’ll stick with a situation where exams are each 5% of your final grade. Let’s say you earned 36 of 45 possible points on an exam for a grade of 0.8, or 80%. If we multiply that score by the assignment weight, then we will have effectively reweighed the assignment’s score in terms of the overall course grade. When we multiply the exam score of 0.8 by the exam weight of 0.5 we get 0.04, meaning you just earned 4 percentage points towards your final grade. A perfect score would have netted you the full 5 percentage points. Thus, another way to look at your score of 0.8 is that you’ve lost 1 percentage point on your final grade. In general, we can assess the positive impact of a score by multiplying that score by the assignment weight. The negative impact is then the difference between the assignment weight and the positive impact.
One of the best ways to contextualize this kind of information is to look at what this means in terms of your minimum and maximum grade for the course. Say an assignment has a weight of 10% and you achieved a 72% on that assignment. We know this means you’ve earned 7.2, or lost 2.8, percentage points towards your final course grade. Thus, your final grade can be no lower than a 7.2% and no higher than a 97.2%. When you’re dealing with assignments with a very large weight, say greater than 10%, then this can cap your grade by as much as a full letter grade. On the other hand, an average assignment might not mean much more than the difference between a straight B and a B+.
What’s my grade?
If you can compute the impact of a single assignment, then you can compute your current grade. Let’s say you’ve had three assignments with weights of 12%, 5%, and 8% and with scores of 85%, 100%, and 72%, respectively. First we notice that 25% of the total grade is accounted for by these three assignments. We get this by summing the assignment weights. Now we want to see how many of those percentage points we’ve earned and lost so far. The first assignment netted us 10.2 percentage points, the second 5, and the third 5.76. Again, we get this by multiplying weights and scores. Adding these together we see that we’ve earned 20.96 of 25 possible points for a current grade of 83.84%. This also means our final grade will be no lower than 20.96% but no higher than 95.04% because we’ve lost 4.04 percentage points on these assignments. So long as you keep track of all your assignment scores and weights, you can continue to recompute your grade all semester and you can continue to narrow down the range of possible grades by tracking points gained and lost.