Statistics - Interpreting and Evaluating Statistical Representations

Statistics - Interpreting and Evaluating Statistical Representations

IP 1
5 marks

Forty students completed a puzzle. Their completion times are summarised below.

Completion time, \(t\) (minutes)Frequency
\(0<t\leq10\)\(6\)
\(10<t\leq20\)\(a\)
\(20<t\leq30\)\(14\)
\(30<t\leq40\)\(b\)

  1. Exactly \(25\%\) of the students took more than 30 minutes. Find \(a\) and \(b\).

    [3]

  2. Lina says, “The modal completion time is 25 minutes because 25 is the midpoint of the class with the greatest frequency.”

    Explain why Lina’s conclusion is not justified. State what can be concluded about the modal class.

    [2]

Solution:

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Answer:(a) \(a=10,\ b=10\) (b) The exact mode cannot be determined; the modal class is \(20<t\leq30\).

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