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Nov 2017 p61 q2
2463
The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summarised in the following table.
Time (seconds)
3 – 5
6 – 8
9 – 11
12 – 16
17 – 25
Frequency
10
15
17
4
2
(i) On the grid, draw a cumulative frequency graph to represent this information. [3]
(ii) 35 of these cars accelerated from 0 to 30 metres per second in a time more than \(t\) seconds. Estimate the value of \(t\). [2]
Solution
(i) To draw the cumulative frequency graph, calculate the cumulative frequencies:
Plot these cumulative frequencies against the upper class boundaries: (5.5, 10), (8.5, 25), (11.5, 42), (16.5, 46), (25.5, 48).
(ii) To find \(t\), note that 35 cars accelerated in more than \(t\) seconds, so 13 cars accelerated in \(t\) seconds or less. From the cumulative frequency graph, find the time corresponding to a cumulative frequency of 13. This gives \(t \approx 6.5\) seconds, so \(6 < t < 7\).