2025 IGCSE 0580 May/June P22 Q13

11 marks

\(100\) students solve a puzzle.
The table shows information about the time taken by each student to solve the puzzle.
Time (\(t\) seconds) \(20<t\le40\) \(40<t\le60\) \(60<t\le100\)
Frequency \(30\) \(40\) \(30\)
1. Work out an estimate of the mean.[4]
2. Complete the histogram to show the information in the table.[2]
\(80\) adults solve the same puzzle as the students.
The cumulative frequency table shows information about the time taken by each adult to solve the puzzle.
Time (\(t\) seconds) \(t\le20\) \(t\le40\) \(t\le60\) \(t\le80\) \(t\le100\) \(t\le120\)
Cumulative frequency \(0\) \(12\) \(36\) \(60\) \(74\) \(80\)
1. On the grid, draw a cumulative frequency diagram.[3]
2. Use your cumulative frequency diagram to find an estimate for
  1. the median[1]
  2. the lower quartile.[1]

Time (\(t\) seconds)	\(20<t\le40\)	\(40<t\le60\)	\(60<t\le100\)
Frequency	\(30\)	\(40\)	\(30\)

Time (\(t\) seconds)	\(t\le20\)	\(t\le40\)	\(t\le60\)	\(t\le80\)	\(t\le100\)	\(t\le120\)
Cumulative frequency	\(0\)	\(12\)	\(36\)	\(60\)	\(74\)	\(80\)

Solution:

Solution locked

Similar questions are unavailable for this question.

Answer:(a)(i) \(53\text{ s}\). (ii) Bar heights \(1.5,2,0.75\). (b)(i) Increasing cumulative frequency curve through the six given points. (ii)(a) Approximately \(63\text{ s}\). (b) Approximately \(47\text{ s}\).

Need help? Join our JC Math tuition classes.

Learn more