The table below shows the frequency distribution of the marks scored by fifty students in...
MATHEMATICS
WAEC 1993
The table below shows the frequency distribution of the marks scored by fifty students in an examination.
| 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.
Explanation
| Marks | Upper class boundary | 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
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