When calculating grade averages, you may encounter two basic types of average - arithmetic and weighted. Both are useful, but are used in different situations. Let's explain the difference between them.
Arithmetic average is the simplest type of average. It's calculated by adding all values together and dividing by the number of values. All values have equal weight.
Average = (Value1 + Value2 + ... + ValueN) / N
Weighted average takes into account that some values are more important than others. Each value has its weight, which determines how much it affects the final average.
Weighted Average = (Value1 × Weight1 + Value2 × Weight2 + ...) / (Weight1 + Weight2 + ...)
- Arithmetic average: All values have equal importance
- Weighted average: Different values have different importance (weight)
- Usage: Arithmetic for equal grades, weighted when e.g., a written test has greater weight than oral examination
Imagine you have grades 1, 2, and 3. The arithmetic average is (1+2+3)/3 = 2.0.
But if grade 3 was from a more important written test (weight 2) and other grades have weight 1, the weighted average is (1×1 + 2×1 + 3×2) / (1+1+2) = 9/4 = 2.25.
Use arithmetic average when all grades are equal. Use weighted average when different grades have different importance - for example, written tests have greater weight than small quizzes or oral examinations.