Mathematics
Grade average calculator
Simple average, weighted average, and the question that actually matters: what mark do I need next time to reach the average I want.
Simple average, weighted average and the mark you need
A simple average treats every mark alike: add them and divide by how many there are. A weighted average gives each one a weight, and that is what many schools actually apply, counting written papers double or giving end-of-term tests more weight. The difference between the two can be half a point, and therefore a whole grade on a report.
The most useful question, though, is the third one: what mark is needed next time. The calculation is not intuitive because the new assessment does not merely join the average, it lengthens it: if you have five marks averaging 6.4 and add one more, the final average is worked out over six marks. To reach 7 the total has to be 42, and so far it is 32, so the mark needed is 10.
That same mechanism explains why recovering gets harder as the year goes on. Each new mark carries an ever smaller fraction of the total: with three marks behind you a top mark moves things a lot, with twelve it barely registers. It is a mathematical point rather than a motivational one, and knowing it helps you judge when to ask for more assessments rather than staking everything on one.
Common mistakes
- Averaging the averages: the first-term average and the second-term one cannot be averaged together if the terms hold different numbers of marks. You have to go back to the individual marks.
- Forgetting that the new mark lengthens the average: to move from 6.4 to 7 it is not enough to score 7, because the average is recomputed over one more mark.
- Using a simple average when the school uses a weighted one: it is worth checking which weights are actually set in the electronic register.
Frequently asked questions
How do you calculate a grade average?
Add all the marks and divide by how many there are. With 6, 7, 5.5, 8 and 7 the sum is 33.5 and the average is 6.7.
How does a weighted average work?
Multiply each mark by its weight, add the products and divide by the sum of the weights. A 6 of weight 1 and an 8 of weight 3 give (6 + 24)/4 = 7.5, not 7.
What mark do I need to reach a given average?
Multiply the target average by the total number of marks you will have, subtract the sum of the marks so far and divide by the number of remaining assessments. The answer can exceed the top of the scale, and then the target is not reachable with those assessments.
Why is it harder to raise an average when you have many marks?
Because each new mark carries 1 divided by the total number of marks. With four marks the fifth carries a fifth of the average, with fifteen marks the sixteenth carries a sixteenth: the same top mark moves far less.
How this calculation works
Simple average of n marks: M = (v₁ + v₂ + … + vₙ)/n. Weighted average with weights p₁…pₙ: M = Σ(vᵢ·pᵢ)/Σpᵢ. The simple average is the special case where every weight is 1. Mark needed: if the current average is M over n marks, the current total is M·n; to reach a target average T with u assessments still to come, all scoring the same mark x, set (M·n + u·x)/(n + u) = T, giving x = [T·(n + u) − M·n]/u. The answer can fall outside the marking scale, which means the target is not reachable with that number of assessments.