How to Average Percentages Correctly
Percentages are ratios with a base of 100. Because they are relative metrics, you cannot always average them by simply adding them up and dividing by the count. Doing so assumes that all the base quantities are identical, which is rarely the case in practical applications.
Simple Average vs. Weighted Average
A Simple Average is appropriate when all percentages are of equal weight. For example, if you get 90%, 80%, and 70% on three homework assignments that are all worth exactly 10 points each, your average homework grade is simply:
(90% + 80% + 70%) ÷ 3 = 80.00%
However, if your grade is split between Homework (worth 20% of your total grade) and Exams (worth 80% of your grade), and you got 95% on homework and 70% on exams, you cannot average them to 82.5%. You must use a Weighted Average because the exams are worth four times as much:
Weighted Average = [ (95% × 20) + (70% × 80) ] ÷ (20 + 80)
Weighted Average = [ 1900 + 5600 ] ÷ 100 = 75.00%
Calculating weighted averages prevents grading surprises, investment calculation mistakes, and statistics errors. Adjust rows and weights in our calculator to model your averages step-by-step.
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