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Five numbers from their mean, median and mode

Five numbers from their mean, median and mode

IP 1
6 marks

Five positive integers have mean \(8\), median \(9\) and a single mode of \(10\).

  1. Explain why the two largest numbers must both be \(10\).[2]
  2. Find all the possible sets of five numbers.[3]
  3. Find the largest possible range.[1]

Solution:

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Answer:(a) median \(c=9\), so only \(d\) and \(e\) can be \(10\) (b) \(3,8,9,10,10\); \(4,7,9,10,10\); \(5,6,9,10,10\) (c) \(7\)

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