Statistics - Finding Unknowns from Averages and Spread

Statistics - Finding Unknowns from Averages and Spread

IP 1
5 marks

The table shows the time a group of students spent practising a musical instrument on Monday. The value of \(x\) is a non-negative integer.

Practice time (minutes)\(10\)\(20\)\(30\)\(40\)
Number of students\(8\)\(x\)\(3\)\(2\)

  1. Find the greatest possible value of \(x\) for which the median practice time is \(10\) minutes. Justify your answer.

    [3]

  2. A student claims, “For some value of \(x\), the mean practice time will be exactly \(20\) minutes.”

    Is the claim correct? Justify your answer.

    [2]

Solution:

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Answer:(a) \(x=2\) (b) No; the mean is always less than \(20\) minutes.

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