Weighted Average Formula — Practical Examples

The weighted average formula is one of the most useful mathematical tools in academics and professional life. Its general form is:

x̄ = (w₁x₁ + w₂x₂ + ... + wₙxₙ) ÷ (w₁ + w₂ + ... + wₙ)

Where:

• x̄ = Weighted average
• x = Each individual value or grade
• w = Weight assigned to each value
• n = Total number of elements

Grades: Midterm 1 = 7.5 (25%), Midterm 2 = 8.0 (25%), Final Exam = 9.5 (50%)

(7.5×25 + 8.0×25 + 9.5×50) ÷ (25+25+50) = (187.5 + 200 + 475) ÷ 100 = 862.5 ÷ 100 = 8.63

Courses with credit hours: Calculus 8.5 (4 credits), Physics 7.0 (3 credits), Chemistry 9.0 (2 credits)

(8.5×4 + 7.0×3 + 9.0×2) ÷ (4+3+2) = (34 + 21 + 18) ÷ 9 = 73 ÷ 9 = 8.11

• Forgetting to divide by the sum of weights: Multiplying grades by weights and adding them is only half the calculation. Always divide by the total weight.
• Mixing decimal and percentage weights: Using 30% as 30 works, but using 0.30 in the same calculation will give a different result. Stay consistent.
• Adding weights incorrectly: Verify that every weight in the numerator is also included in the denominator.