Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The table shows the marks of candidates in an exam.
| Marks | Candidates |
|---|---|
| 0-20 | 6 |
| 20-40 | 14 |
| 40-60 | 26 |
| 60-80 | 22 |
| 80-100 | 12 |
The top candidates get a distinction, and the examiner has to announce the lowest mark that earns one. The examiner also wants to tell the parents how many candidates scored fewer than marks. Assume that the candidates are spread evenly through each class. Find both numbers.
Read a cumulative frequency curve at the height for the median, at and for the quartiles, and at for the th percentile. With straight segments, a reading at the height is in the class where the running total reaches .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The running totals. at the limits .
Step 2. The cut-off. candidates are below it. The height lies in the class to , where the running total goes from to . So the cut-off is marks.
Step 3. Fewer than . At marks the total is . The class to has candidates, and is halfway through it, so we add . The total is .
Answer: the lowest mark for a distinction is , and candidates scored fewer than .
Check. At marks the curve is at , so candidates are above it.
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