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Mathematics · Grades 9–12

Weighted mean

Multiply each value by its frequency; divide by total frequency, not by the number of values.

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The key idea

Multiply each value by its frequency; divide by total frequency, not by the number of values.

weighted mean = Σ(wᵢxᵢ)/Σwᵢ

Worked examples

A score of 11 occurs 10 times; a score of 20 occurs 9 times. Find the mean as a fraction or decimal.

(11 × 10 + 20 × 9)/(10 + 9) = 290/19

290/19

A score of 29 occurs 4 times; a score of 29 occurs 3 times. Find the mean as a fraction or decimal.

(29 × 4 + 29 × 3)/(4 + 3) = 29

29

Try it yourself

  1. A score of 18 occurs 1 times; a score of 6 occurs 6 times. Find the mean as a fraction or decimal.

  2. A score of 13 occurs 10 times; a score of 30 occurs 1 times. Find the mean as a fraction or decimal.

Check your understanding

Answers and marking notes
  1. 54/7

    (18 × 1 + 6 × 6)/(1 + 6) = 54/7

  2. 160/11

    (13 × 10 + 30 × 1)/(10 + 1) = 160/11

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.