A weighted average gives some values more influence over the final mean than others. In academics, this matters whenever subjects, courses or assessment components carry different credits, weightings or maximum marks.
The formula:
Weighted Average = Σ (Value × Weight) / Σ Weights
Compare this with a simple (arithmetic) average, which assumes every value has weight 1 — appropriate only when each item should contribute equally.
In practice you encounter weighted averages every time you compute:
• A semester GPA where courses have different credit values. • An IGNOU final grade where assignments count for 30% and the term-end exam counts for 70%. • A weighted-coursework grade where labs are 25%, midterm 30%, final 45%. • An aggregate medical-entrance score where MDCAT (50%), FSc (40%) and Matric (10%) contribute by published weights.
When weights sum to 1 (i.e. they are fractions, not raw credit values), the formula simplifies to Σ (Value × Weight). Both forms are equivalent — Σ Weights = 1 in that case.
A common error is forgetting to divide by the sum of weights when weights are raw counts rather than fractions. Always verify which form is in use before computing.