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June 2022 p53 q1
2484
The time taken, \(t\) minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table.
Time taken \((t)\) minutes
\(t \le 25\)
\(t \le 50\)
\(t \le 75\)
\(t \le 100\)
\(t \le 150\)
\(t \le 200\)
Cumulative frequency
16
44
86
104
132
150
Draw a cumulative frequency graph to illustrate the data.
Use your graph to estimate the 20th percentile of the data.
Solution
(a) To draw the cumulative frequency graph, plot the points:
\((25, 16)\), \((50, 44)\), \((75, 86)\), \((100, 104)\), \((150, 132)\), \((200, 150)\),
and connect them smoothly, starting from \((0, 0)\).
(b) The 20th percentile corresponds to
\(0.2 \times 150 = 30\) on the cumulative frequency axis.
Draw a horizontal line from the cumulative frequency of \(30\) to the curve,
then drop a vertical line to the \(t\)-axis.
The \(t\)-value at this point is approximately \(40\) minutes.