Weighted vs. Arithmetic Average: The Difference

Why the simple average is often wrong.

In school, not every grade counts equally. While the arithmetic average treats all grades equally, the weighted average considers the importance (weighting) of each individual grade.

Calculate grade average

The Arithmetic Average (Simple Mean)

This is the classic average: You add all grades and divide by their count. This is used when all exams are worth exactly the same.

(Grade A + Grade B + Grade C) / 3

When to use?

  • All tests have the same importance
  • Quick rough calculation
  • When the teacher explicitly says so
Arithmetic Average

The Weighted Average

Here each grade has a 'factor' (e.g., 0.5, 1, or 2). A grade with weight 2 counts twice as much as a grade with weight 1. This is crucial for the report card grade.

Sum (Grade × Weight) / Sum of Weights

When to use?

  • Major exams count more than small tests
  • Core subjects count double (e.g., for report card)
  • University ECTS credit calculation
Weighted Average

Calculation Example

You have a 6.0 on a small test (weight 0.5) and a 4.0 on a major exam (weight 2).

Arithmetic
(6.0 + 4.0) / 2
= 5.0✗
Weighted
(6.0 × 0.5 + 4.0 × 2) / 2.5
= 4.4✓

The difference is huge: 5.0 vs. 4.4. The weighted average is reality because the worse grade was weighted much more heavily.

Conclusion

Never rely on the simple average when your teachers use different weightings. Use our calculator to determine the true value.

Frequently Asked Questions About Averages

How do I know what weighting my exam has?
The weighting is usually communicated by the teacher at the beginning of the semester. Ask if you're unsure. Typical values are: Small tests = 0.5, Normal work = 1, Major exams = 2.
Can I compensate a major exam with a small test?
Only with difficulty. If the major exam has weight 2 and the small test only 0.5, you need 4 small tests with top grades to compensate for one poor major exam.
Why is the weighted average worse in my case?
Because your worse grades were probably in exams with higher weighting. That has more influence on the overall result.
Does the Matura preliminary grade count double?
That depends on the canton. In many cantons, the Matura grade and the experience grade (preliminary grade) are combined, often in equal parts (50/50).