The following table shows the frequency distribution of marks obtained by students of a class:

Class Interval
Frequency
0-10
2
10-20
5
20-30
8
30-40
12
40-50
15
50-60
20
60-70
18
70-80
17
80-90
16
90-100
2

Based on this information, the median from the graph is,

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50.5

56.5

55.5

57.5

answer is D.

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Detailed Solution

Given frequency table is,

Class Interval	Frequency
0-10	2
10-20	5
20-30	8
30-40	12
40-50	15
50-60	20
60-70	18
70-80	17
80-90	16
90-100	2

Consider the table,

Class Interval	Frequency (f)	Cumulative frequency
0-10	2	Less than 10	2
10-20	5	Less than 20	7
20-30	8	Less than 30	15
30-40	12	Less than 40	27
40-50	15	Less than 50	42
50-60	20	Less than 60	62
60-70	18	Less than 70	80
70-80	17	Less than 80	97
80-90	16	Less than 90	113
90-100	2	Less than 100	115

To represent less than type ogive, we have to plot the points

10, 2, 20, 7, 30, 15, 40, 27, 50, 42, 60, 62, 70, 80, 80, 97, 90, 113, 100, 115

on the graph paper and join them by free hand to get a smooth curve, which is the required less than type ogive.
Now, the table for more than ogive will be,

Class Interval	Frequency (f)	Cumulative frequency
0-10	2	More than 0	115
10-20	5	More than 10	113
20-30	8	More than2	108
30-40	12	More than 30	100
40-50	15	More than 40	88
50-60	20	More than 50	73
60-70	18	More than 60	53
70-80	17	More than 70	35
80-90	16	More than 80	18
90-100	2	More than 90	2

To represent less than type ogive, we have to plot the lower limit on the x-axis and corresponding cumulative frequency on the Y-axis, i.e. (0,115), (10,113),

20, 108, 30, 100, 40, 88, 50, 73, 60, 53, 70, 35, 80, 18, 90, 2

on the graph paper and join them by free hand to get a smooth curve, which is the required less than type ogive.
We know,
Where the two ogives intersect, the x-coordinate is known as the median of the data.
The Less than and more than ogive on the same axis is given as,
Question Image

The two ogive intersect at a point, whose x-coordinate is 57.5.
So, the median is 57.5.
Therefore, the median of the given data is 57.5.
Hence, option 4 is correct.

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