The table shows the distribution of marks obtained by 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 |
| Frequency | 7 | 11 | 17 | 20 | 29 | 34 | 30 | 25 | 21 | 6 |
(a) Construct a cumulative frequency table for the distribution.
(b) Draw the cumulative frequency curve for the distribution.
(c) Using the curve, find correct to one decimal place, the:
(i) median mark;
(ii) lowest mark for the distinction if 5% of the students passed with distinction
Explanation
| Marks |
Upper Class Boundary |
Frequency (F) |
Cumulative Frequency (F) (CF) |
|
0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 |
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5 |
7 11 17 20 29 34 30 25 21 6 |
7 18 35 55 84 118 148 173 194 200 |
(b)
(c) (I) Median Mark = 54.5
(ii) Lowest mark, if 5% of the students passed = 14