AQA · Mathematics · 8300
GCSE Maths: Averages: combined mean
Statistics · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Averages: combined mean (Corbettmaths Video 53), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the formula for calculating combined mean when you know the number of items and mean of each group?
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Combined mean = (sum of all values) ÷ (total number of items), where sum of all values = (n₁ × mean₁) + (n₂ × mean₂) + ... for each group.
If 20 houses have a mean of 1.5 cars and 80 houses have a mean of 2 cars, what is the combined mean number of cars per house?
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1.9 cars per house. Calculate: (20 × 1.5 + 80 × 2) ÷ 100 = (30 + 160) ÷ 100 = 1.9
If you know the combined mean of all items and the mean of some groups, how can you find the mean of the remaining group?
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Rearrange the formula: (mean of unknown group) = [(total items × combined mean) - (sum of known groups)] ÷ (number in unknown group)
If 25 students scored a mean of 81% and 15 students scored a mean of 87%, what is the combined mean score for all 40 students?
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83.25%. Calculate: (25 × 81 + 15 × 87) ÷ 40 = (2025 + 1305) ÷ 40 = 3330 ÷ 40 = 83.25%
When solving a combined mean problem involving ratios, what must you do before applying the combined mean formula?
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Convert the ratio to actual numbers using the total given. For example, if 30 students are in ratio 2:3, that's 12 boys and 18 girls (since 2+3=5 parts, 30÷5=6 per part).
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