4024/12 Oct/Nov 2021, Question 13: Mean, Median, Mode and Range
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Five numbers have mean 17, listed smallest to largest. The three smallest are equal, the middle three sum to 35, and the largest is four times the smallest. Find all five numbers in order.
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Solution · 3 marks
- 1Total = 5 × 17 = 85
- 2Numbers a, a, a, b, 4a with a + a + b = 35, so b = 35 − 2a
- 33a + b + 4a = 85 → 7a + 35 − 2a = 85 → 5a = 50 → a = 10
- 4b = 35 − 20 = 15, largest = 4 × 10 = 40
- 5Numbers: 10, 10, 10, 15, 40
Answer10, 10, 10, 15, 40
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