Weighted grades: how to work out what you actually need

The mistake is averaging percentages instead of weighting them

Take an assessment breakdown that is common enough to be familiar: coursework worth 40%, a midterm worth 20%, and a final worth 40%. Suppose coursework scored 72% and the midterm 65%.

The instinctive move is to average 72 and 65, giving 68.5%. That figure is not your grade and it does not predict your grade, because it treats a 40% assessment and a 20% assessment as equally important when one is worth twice the other.

The gap here is small, and it is not always small — it widens exactly in proportion to how differently weighted the assessments are, and it is worst when a heavy assessment has an unusual score. A 90% on something worth 5% moves your grade far less than a 70% on something worth 50%, and no average of the two percentages shows that.

Weighted grade = the sum of each score multiplied by its weight, divided by the sum of the weights you are counting. The division by the summed weights is what makes it correct partway through a course, when the later assessments have not happened yet.

The question people actually want answered

Most people are not asking what their current grade is. They are asking what they need on the remaining assessment. That is a different calculation, and it is solvable in one line.

• Points already earned = sum of each completed score × its weight
• Points remaining = the sum of the weights of everything still to come
• Score needed = (target − points already earned) ÷ points remaining

Continuing the example above: coursework at 72% is worth 0.40 × 72 = 28.8 points, and the midterm at 65% is worth 0.20 × 65 = 13 points. That is 41.8 points banked out of the 60 available so far. The final is worth the remaining 40 points.

That last row is the useful one and it is the reason to do this calculation early rather than the night before. A target can become arithmetically unreachable before the final is written, and at that point the choice is between a different target and a different course of action entirely — not more revision.

Notice also how steeply the requirement climbs. Ten percentage points on the target costs more than thirty points on the final, because the final is only 40% of the grade. Weighting cuts both ways.

Weights that do not add up to 100%

Weightings that sum to less than 100 are common in continuous assessment and almost always mean one of two things: assessments that have not been added to the scheme yet, or a scheme where the weights describe relative importance rather than fixed proportions.

This matters because it changes which formula is correct. Dividing by the sum of the weights you have counted gives a percentage-of-work-graded, which is the right answer for tracking your progress. Not dividing gives points out of a total that has not been reached yet, which is the right answer if the weights are fixed proportions of a final grade.

Weights summing to more than 100 are usually a data-entry error, and occasionally a scheme where a component is counted twice. Either way it is worth resolving before you trust any grade calculated from it.

Dropping the lowest score re-weights everything

A scheme that drops your worst assessment does not simply remove that score. It removes that score and its weight, which increases the relative influence of everything else.

So dropping a weak 10% assessment raises your final grade by more than the assessment's own weight suggests, because the remaining assessments now make up the full 100%. It is worth recalculating rather than estimating, and it is worth doing before a low score is banked rather than after.

Where students most often go wrong

1. Averaging percentages that carry different weights, which is the error at the top of this article.
2. Forgetting to divide by the weight of the work completed so far, which understates the current standing partway through a course.
3. Assuming the final is worth its face value when an earlier assessment has been dropped, which changes every remaining weight.
4. Treating a target as fixed. The useful question is not 'what do I need' but 'what is still reachable, and what do I want given that'.

What to do with the answer

The number this calculation produces is only useful if it changes what you do next, and it usually points one of three ways.

• An easy target. The requirement sits well inside what you have been scoring, and the risk is complacency rather than arithmetic.
• A target needing a strong result. The requirement is above your recent average, which means something has to change — more revision, different revision, or help. Knowing the size of the gap is what makes the change specific rather than vague.
• A target that is already unreachable. No score on the remaining assessment produces the grade. This is the most useful output of the three, because it arrives while there is still time to choose a different target or a different approach to the same course.

Presented that way, the calculation is not a source of anxiety but a way of replacing an assumption with a fact — and a fact is something you can act on. The alternative is finding out after the exam, which is the only version of this that costs you anything.

Work out your own position in a few seconds

The Grade & Final Exam Planner takes the assessments, their weights and your scores, and returns your current standing on a weighted basis alongside the score required on each remaining assessment for a range of target grades — including telling you plainly when a target is no longer mathematically reachable.