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Question
Draw ogive of both the types for the following frequency distribution and hence find median.
| Marks | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| No. of students | 5 | 5 | 8 | 12 | 16 | 15 | 10 | 8 | 5 | 2 |
Solution
| Marks | No. of students | Less than cumulative frequency (c.f.) |
More than cumulative frequency (c.f.) |
| 0 – 10 | 5 | 5 | 86 |
| 10 – 20 | 5 | 10 | 81 |
| 20 – 30 | 8 | 18 | 76 |
| 30 – 40 | 12 | 30 | 68 |
| 40 – 50 | 16 | 46 | 56 |
| 50 – 60 | 15 | 61 | 40 |
| 60 – 70 | 10 | 71 | 25 |
| 70 – 80 | 8 | 79 | 15 |
| 80 – 90 | 5 | 84 | 7 |
| 90 – 100 | 2 | 86 | 2 |
For less than given points to be plotted are (10, 5), (20, 10), (30, 18), (40, 30), (50, 46), (60, 61), (70, 71), (80, 79), (90, 84), (100, 86)
For more than given points to be plotted are (0, 86), (10, 81), (20, 76), (30, 68), (40, 56), (50, 40), (60, 25), (70, 15), (80, 7), (90, 2)
From the point of intersection of two ogives. We draw a perpendicular on X-axis.
The point where it meets the X-axis gives the value of the median.
∴ Median ≈ 48
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