The data shows the marks obtained by students in a biology test
| 52 | 56 | 25 | 56 | 68 | 73 | 66 | 64 | 56 | 48 |
| 20 | 39 | 9 | 50 | 46 | 54 | 54 | 40 | 50 | 96 |
| 36 | 44 | 18 | 97 | 65 | 21 | 60 | 44 | 54 | 32 |
| 92 | 49 | 37 | 94 | 72 | 88 | 89 | 35 | 59 | 34 |
| 15 | 88 | 53 | 16 | 84 | 52 | 72 | 46 | 60 | 42 |
(a) Construct a frequency distribution table using the class interval 0 – 9, 10 – 19, 19, 20, 29…
(b) Draw a cumulative frequency curve for the distribution
(c) Use the graph to estimate the;
(i) median
(ii) Percentage of students who scored at least 66 marks, correct to the nearest whole number.
Explanation
|
Class Intervals |
Class Boundaries |
Frequency |
Cumulative Frequency |
| 0 - 9 | 0.5 - 9.5 | 1 | 1 |
| 10 - 19 | 9.5 - 19.5 | 3 | 4 |
| 20 - 29 | 19.5 - 29.5 | 3 | 7 |
| 30 - 39 | 29.5 - 39.5 | 6 | 13 |
| 40 - 4921 | 39.5 - 49.5 | 8 | 21 |
| 50 - 59 | 49.5 - 59.5 | 12 | 33 |
| 60 - 69 | 59.5 - 69.5 | 6 | 39 |
| 70 - 79 | 69.5 - 79.5 | 3 | 42 |
| 80 - 89 | 79.5 - 89.5 | 4 | 46 |
| 90 - 99 | 89.5 - 99.5 | 4 | 50 |
| \(\sum f = 50\) |
(b)
(c) (I) Mean mark = 49.9
(ii) Percentage of at least 66 mark = \(\frac{13}{50} \times 100\)%
= 26%