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Using less than ogive for the following frequency distribution the median is,

Marks obtained
10-20
20-30
30-40
40-50
50-60
60-70
70-80
No. of Students
3
4
3
3
4
7
9

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68.75.

60.75.

58.75.

59.75.

answer is C.

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Detailed Solution

Given table is,

Marks obtained	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of Students	3	4	3	3	4	7	9

Consider the table,

Marks Obtained	No. Of Students	Cumualtive Frequency
10-20	3	Less than 20	3
20-30	4	Less than 30	7
30-40	3	Less than 40	10
40-50	3	Less than 50	13
50-60	4	Less than 60	17
60-70	7	Less than 70	24
70-80	9	Less than 80	33

To draw the less than type ogive, we plot

20, 3, 30, 7, 40, 10, 50, 13, (60, 17) (70, 24) (80, 33)

on the graph and join them by freehand. The graph obtained will be the required less than type graph.
Question Image

Here, N = 33.
So,

N 2 = 16.5

We locate the point on the ogive whose y-coordinate is 16.5. The x-coordinate of that point is the median.
Question Image

The x-coordinate of that point is 58.75. So, the median is 58.75.
Therefore, the required median is 58.75.
Therefore, option 3 is correct.

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