When calculating averages, you encounter two types: the arithmetic average and the weighted average. While both are useful, they are used for different purposes. In this article, we explain the difference.
The arithmetic average
The arithmetic average (also called 'simple average') is the sum of all values divided by the number of values. Each value counts equally.
Arithmetic average = (value₁ + value₂ + ... + valueₙ) / n
Example: With grades 6, 7 and 8, the arithmetic average is (6+7+8)/3 = 7.0
The weighted average
The weighted average takes into account the relative importance of each value. Values with higher weight have more influence on the final result.
Weighted average = Σ(value × weight) / Σ(weight)
Example: Grade 6 (weight 1), 7 (weight 2), 8 (weight 3). Weighted average = (6×1 + 7×2 + 8×3)/(1+2+3) = (6+14+24)/6 = 7.33
The main difference
The difference between both averages:
- Arithmetic average: all values are equal, none count more heavily
- Weighted average: some values count more heavily than others
- With equal weights (all 1), the weighted average equals the arithmetic average
When do you use which?
Use arithmetic average when:
- All values are equally important
- Quick calculation without weights
- Daily calculations (average temperature, average score)
Use weighted average when:
- School grades with different weights (exam vs quiz)
- University credit points (ECTS)
- Financial calculations (portfolio weighted return)
What does your school use?
Most Dutch secondary schools use the weighted average. Exams usually weigh more than written quizzes or homework checks.
Check your school's PTA (Program of Testing and Completion) to see which weights apply for each subject.
Note: Magister and SOMtoday automatically calculate your weighted average based on the configured weights.
Calculate both averages
Use our calculator to calculate both your weighted and arithmetic average. Enter your grades - with or without weights - and see the result immediately.