The table below shows the frequency distribution of the marks scored by fifty students in an examination.
(a) Draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.
| Marks (%) | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |
| Freq | 2 | 3 | 4 | 6 | 13 | 10 | 5 | 3 | 2 | 2 |
(a) Draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.
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Correct Answer: Option n
Explanation:
(a)
(b)(i) Upper quartile \(Q_{3}\) = 57 marks
(ii) Pass mark if 60% of the class passed = 42 marks
| Marks | Upper classboundary | Freq | Cum Freq |
| 0-9 | 9.5 | 2 | 2 |
| 10-19 | 19.5 | 3 | 5 |
| 20-29 | 29.5 | 4 | 9 |
| 30-39 | 39.5 | 6 | 15 |
| 40-49 | 49.5 | 13 | 28 |
| 50-59 | 59.5 | 10 | 38 |
| 60-69 | 69.5 | 5 | 43 |
| 70-79 | 79.5 | 3 | 46 |
| 80-89 | 89.5 | 2 | 48 |
| 90-99 | 99.5 | 2 | 50 |
(a)
(b)(i) Upper quartile \(Q_{3}\) = 57 marks
(ii) Pass mark if 60% of the class passed = 42 marks