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Median of the following frequency distribution.

$x_{i}$
3
6
10
12
7
15
$f_{i}$
3
4
2
8
13
10

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7

10

8.5

of these

answer is C.

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Detailed Solution

Given data,

$x_{i}$	3	6	10	12	7	15
$f_{i}$	3	4	2	8	13	10

We arranged the value of variate

x_{i}

in ascending order with their frequencies.

$x_{i}$	3	6	7	10	12	15
c.f.	3	7	20	22	30	40

Here

N = 40

(even)

Median = \frac{(\frac{N}{2}) th term + (\frac{N}{2} + 1) th term}{2}

\Rightarrow Median = \frac{(20) th term + (21) th term}{2}

\Rightarrow Median = \frac{7 + 10}{2}

\Rightarrow Median = \frac{17}{2}

\Rightarrow Median = 8.5

Thus, the median of the given data is 8.5.
Hence, the correct option is 3.

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