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Question
The marks obtained by 100 students of a class in an examination are given below.
| Mark | No. of Student |
| 0 - 5 | 2 |
| 5 - 10 | 5 |
| 10 - 15 | 6 |
| 15 - 20 | 8 |
| 20 - 25 | 10 |
| 25 - 30 | 25 |
| 30 - 35 | 20 |
| 35 - 40 | 18 |
| 40 - 45 | 4 |
| 45 - 50 | 2 |
Draw 'a less than' type cumulative frequency curves (ogive). Hence find the median.
Solution
We first prepare the cumulative frequency table by less than method as given below–
| Marks | No. of students | Marks less than | Cumulative Frequency |
| 0 - 5 | 2 | 5 | 2 |
| 5 - 10 | 5 | 10 | 7 |
| 10 - 15 | 6 | 15 | 13 |
| 15 - 20 | 8 | 20 | 21 |
| 20 - 25 | 10 | 25 | 31 |
| 25 - 30 | 25 | 30 | 56 |
| 30 - 35 | 20 | 35 | 76 |
| 35 - 40 | 18 | 40 | 94 |
| 40 - 45 | 4 | 45 | 98 |
| 45 - 50 | 2 | 50 | 100 |
Thus we will plot the points (5, 2), (10, 7), (15, 13), (20, 21), (25, 31), (30, 56), (35, 76), (40, 94), (45, 98) and (50, 100).
∴ From the above ogive, the horizontal line drawn from `("N")/(2)=50` intersects the ogive at a point whose x-coordinate is approximately 28.
∴ Hence, Median≈">≈28.
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