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...
Question 1 Report
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
Answer Details
(a) Cumulative Frequency Table
| Marks (%) | Upper Class Boundary | Frequency | Cumulative Frequency |
|---|---|---|---|
| 0 – 9 | 9.5 | 7 | 7 |
| 10 – 19 | 19.5 | 11 | 18 |
| 20 – 29 | 29.5 | 17 | 35 |
| 30 – 39 | 39.5 | 20 | 55 |
| 40 – 49 | 49.5 | 29 | 84 |
| 50 – 59 | 59.5 | 34 | 118 |
| 60 – 69 | 69.5 | 30 | 148 |
| 70 – 79 | 79.5 | 25 | 173 |
| 80 – 89 | 89.5 | 21 | 194 |
| 90 – 99 | 99.5 | 6 | 200 |
(b) Cumulative Frequency Curve
Using the upper class boundaries, plot the points:
(9.5, 7), (19.5, 18), (29.5, 35), (39.5, 55), (49.5, 84),
(59.5, 118), (69.5, 148), (79.5, 173), (89.5, 194) and (99.5, 200).
Join the points with a smooth cumulative frequency curve (ogive).
(c)
(i) Median mark
Total frequency, N = 200.
Median position = N⁄2 = 200⁄2 = 100th value.
The 100th value lies in the class 50
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