Math

Average Percentage Calculator

Find the correct average of two percentages, weighted by their sample sizes.

Calculated Output

Weighted average (%) 70

Simple average (%) 60

Formula: weighted = (p1·n1 + p2·n2) ÷ (n1 + n2)

Step-by-Step Breakdown

1. Values used:

2. Percentage 1 = 40 %

3. Sample size 1 = 50

4. Percentage 2 = 80 %

5. Sample size 2 = 150

7. Weighted average = 70%

8. Simple average = 60%

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The math behind it

Convert each percentage back to a count, add the counts, then divide by the total sample size: (p1·n1 + p2·n2) ÷ (n1 + n2).

40% of 50 and 80% of 150 → (20 + 120) ÷ 200 = 70%, not the naive 60%.

When is the simple average correct?

Only when both groups have the same sample size.