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Mean and median of consecutive numbers

Mean and median of consecutive numbers

IP 1
7 marks
  1. Show that for any five consecutive integers \(n,n+1,n+2,n+3,n+4\), the mean equals the median.[2]
  2. Give an example of five different integers whose mean is not equal to their median.[1]
  3. The mean of seven consecutive even numbers is \(50\). Find the largest of them.[2]
  4. By pairing the first and last terms, show that the mean of the first \(k\) odd numbers \(1,3,5,\ldots,2k-1\) is \(k\).[2]

Solution:

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Answer:(a) both equal \(n+2\) (b) e.g. \(1,2,3,4,20\) (mean \(6\), median \(3\)) (c) \(56\) (d) each end-pair has mean \(k\)

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