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If the median of the following frequency distribution is $28.5$ . find the missing frequencies.

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f_{1}

= 7

f_{2}

= 8

f_{1}

= 8

f_{2}

= 7

f_{1}

= 6

f_{2}

= 9

f_{1}

= 9

f_{2}

= 6

answer is B.

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Detailed Solution

Given that median is 28.5 and the data,
Question Image

We find the cumulative frequency,
Question Image

So median class = 20 - 30 and we have,
45 +

f_{1} + f_{2} = 60

\Rightarrow f_{1} + f_{2} = 15

— (1)
Here,
lower limit of modal class,

(l) = 20

width of modal class,(h)

= 10

c = 5

f = 20

Also,

\frac{N}{2} = \frac{60}{2}

\Rightarrow \frac{N}{2} =

30
So median will be,
Median

= l + (\frac{\frac{N}{2} - c}{f} \times h)

\Rightarrow 8.5 = 20 + (\frac{30 - 5 - f_{1}}{20}) \times 10

\Rightarrow 8.5 = \frac{25 - f_{1}}{2}

\Rightarrow 25 - f_{1} = 17

\Rightarrow f_{1} = 8

Substituting in eq(1),

8 + f_{2} = 15

\Rightarrow f_{2} = 7

f_{1} = 8

and

f_{2} = 7

.
Hence, the correct option is 2.

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