2026 SPS P1 Q10

2026 SPS P1 Q10

Secondary 4
4 marks

The table shows the times, \(t\) minutes, taken by 40 students to complete a Mathematics quiz.

Time, t (minutes)Frequency
\(30\leq t<40\)6
\(40\leq t<50\)10
\(50\leq t<60\)16
\(60\leq t<70\)8
  1. Calculate an estimate for
    1. the mean time,[1]
    2. the standard deviation of the times.[1]
  2. Each recorded time was 5 minutes less than the actual time, so 5 minutes is added to each time to correct it.
    Explain how the mean and standard deviation of the corrected times compare with the values in (a).[2]

Solution:

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Answer:(a) 51.5 min; 9.63 min. (b) Mean increases by 5 min; SD unchanged.

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