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What is the median of the following data?

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73.05

72.54

63.54

91.09

answer is A.

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Detailed Solution

It is given the following frequency distribution table.
Question Image

We first create a cumulative frequency table for the data.

Maths marks	No. of students(f)	Cumulative frequency
60 - 65	8	8
65 - 70	12	20
70 - 75	14	34
75 - 80	8	42
80 - 85	5	47
85 - 90	6	53
90 - 95	4	57
	N = $Σ$ f = 57

We know that,

Median = l + (\frac{\frac{n}{2} - cf}{f}) \times h

From the table, we get

N = 57

⟹ \frac{N}{2} = \frac{57}{2}

⟹ \frac{N}{2} = 28.5

⟹

In the above table

70 - 75

is the median class and the respective c.f. is

20

(cumulative frequency of the class preceding the median class)
According to question,

l = 70

c.f.

= 20

h = l_{2} - l_{1}

⟹ h = 5

f = 14

Putting these values in the formula, we get

Median = l + \frac{\frac{N}{2} - c . f .}{f} \times h

⟹

Median

= 70 + \frac{28.5 - 20}{14} \times 5

⟹

Median

= 73.05

Thus, the median of the data is 73.05.
Hence, the correct option is 1.

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