The weighted average
Section A has 20 learners and a mean mark of 60. Section B has 30 learners and a mean of 70. What is the mean for all fifty?
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Step 1 of 3
- Group A: mean 60, 20 learners. Group B: mean 70, 30 learners.
- Average the two means: (60 + 70) ÷ 2 = 65.
- The true combined mean is 66 — closer to the bigger group.
The rule
The mean for all fifty is 66 marks.
A mean is a total divided equally. So find each section's total first. Call each section a group.
| Section | Learners | Mean | Total marks |
|---|---|---|---|
| A | 20 | 60 | 20 × 60 = 1200 |
| B | 30 | 70 | 30 × 70 = 2100 |
| Together | 50 | 1200 + 2100 = 3300 |
Fifty learners have 3300 marks in all. 3300 ÷ 50 = 66 marks.
The weighted average works in three steps. Multiply each mean by its group size. Add those totals. Divide by the sizes added.
The sizes are the weights. Group A has weight 20. Group B has weight 30.
The halfway guess is (60 + 70) ÷ 2 = 65. That is 1 mark too low. The guess treats the two groups as equal in size.