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Calculate the median in the following frequency distribution

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70

85

83.75

90

answer is D.

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Detailed Solution

Given data,
Question Image

Then,

Median is given by

L + \frac{\frac{n}{2} - c . f .}{f} \times i

where

L

is the lower limit of the median class.
(median class is the class where

{\frac{n}{2}}^{th}

term is lying)

c . f .

is the cumulative frequency of the class preceding the median class

f

is the frequency of the median class,

i

is the class interval of the median class.
From the above table,

L = 70

Also,

\frac{n}{2} = \frac{75}{2}

\Rightarrow \frac{n}{2} = 37.5

c . f . = 15

f = 15

i = 10

Therefore,

median = 70 + \frac{37.5 - 15}{15} \times 10

\Rightarrow median = 70 + \frac{22.5}{15} \times 10

\Rightarrow median = 70 + 7.5 \times 2

\Rightarrow median = 70 + 15

\Rightarrow median = 85

Thus, the median of the given data is 85.
Hence, the correct option is 4.

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