2026 TPSS P2 Q8

2026 TPSS P2 Q8

Secondary 4
7 marks

A study was conducted on the cognitive skills of adults with age. The study recorded the time 80 adults spent solving a number puzzle. The cumulative frequency curve shows the distribution of the time taken.

  1. Use the curve to estimate
    1. the median time taken,[1]
    2. the interquartile range of the time taken.[2]
  2. 20% of the adults took more than \(n\) seconds to solve the puzzle. Find \(n\).[2]
  3. The same group of adults were each given a word puzzle to solve. The box-and-whisker plot shows the distribution of the time taken.
    Make two comparisons between the performances of the adults in solving the two puzzles.[2]

Solution:

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Answer:(a)(i) Approximately 38 s (ii) Approximately 14 s (b) \(n\approx48\) s (c) The number puzzle has a lower median time and a smaller IQR.

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