When calculating grade averages, you may encounter two basic types of averages - arithmetic and weighted. Both are useful but applied in different situations. Let's explain the difference between them.
Arithmetic average is the simplest type of average. It is calculated by summing all values and dividing them by their count. All values have the same 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 resulting average.
Weighted Average = (Value1 × Weight1 + Value2 × Weight2 + ...) / (Weight1 + Weight2 + ...) - Arithmetic average: All values have the same weight
- Weighted average: Different values have different weights (importance)
- Application: Arithmetic for equal grades, weighted when e.g., test has greater weight than oral response
Imagine you have grades 6, 5, and 4. Arithmetic average is (6+5+4)/3 = 5.0.
However, if grade 4 was from an important test (weight 2) and other grades have weight 1, weighted average is (6×1 + 5×1 + 4×2) / (1+1+2) = 19/4 = 4.75.
Use arithmetic average when all grades are equal. Use weighted average when different grades have different importance - for example, tests have greater weight than quizzes or oral responses.