Drawing a curve for race times
Drawing a curve for race times
Secondary 4
8 marks
The table shows the times, \(t\) minutes, taken by \(100\) runners to finish a race.
| Time, \(t\) min | \(20<t\le 25\) | \(25<t\le 30\) | \(30<t\le 35\) | \(35<t\le 40\) | \(40<t\le 45\) |
|---|---|---|---|---|---|
| Frequency | \(8\) | \(22\) | \(35\) | \(25\) | \(10\) |
- Construct a cumulative frequency table.[2]
- On the grid below, using a scale of \(2\) cm to \(5\) minutes on the horizontal axis and \(2\) cm to \(20\) runners on the vertical axis, draw the cumulative frequency curve for \(20\le t\le 45\).[3]
- Use your curve to estimate[3]
- the number of runners who took at most \(33\) minutes,
- the percentage of runners who took more than \(38\) minutes,
- the time \(t\) such that \(70\%\) of the runners took at most \(t\) minutes.
Solution:
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Answer:(a) \(8,30,65,90,100\) at \(25,30,35,40,45\) min (b) Smooth increasing curve through \((20,0),(25,8),(30,30),(35,65),(40,90),(45,100)\) (c)(i) about \(51\) (accept \(48\) to \(54\)) (ii) about \(18\%\) (accept \(15\%\) to \(22\%\)) (iii) about \(36\) min (accept \(35.5\) to \(36.5\))
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