How to find missing frequency in medianFor exampleIf th

| How to find missing frequency in median
For example:
If the median of the distribution given below is 46, find the value of the missing frequencies.

\begin{matrix} V a r i a b l e & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 F r e q u e n c y & 12 & 30 & ? & 65 & ? & 25 & 18 \end{matrix}

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SOLUTION

$\begin{matrix} V a r i a b l e & F r e q u e n c y & C u m u l a t i v e F r e q u e n c y 10 - 20 & 12 & 12 20 - 30 & 30 & 12 + 30 = 42 30 - 40 & f_{1} & 42 + f_{1} 40 - 50 & 65 & 42 + f_{1} + 65 = 107 + f_{1} 50 - 60 & f_{2} & 107 + f_{1} + f_{2} 60 - 70 & 25 & 107 + f_{1} + f_{2} + 25 = 132 f_{1} + f_{2} + f_{1} 70 - 80 & 18 & 132 + f_{1} + f_{2} + 18 = 150 + f_{1} + f_{2} 229 \end{matrix}$
Let $f_{1}$ be the frequency of the class 30 - 40 and $f_{2}$ be the frequency of 50 - 60
Then $f_{1} + f_{2} = T o t a l f r e q u e n c y - S u m o f t h e g i v e n f r e q u e n c y$
$f_{1} + f_{2} = 229 - (12 + 30 + 65 + 25 + 18)$
$= 229 - 150$
$= 79$
Since the given median 46 lies in the class 40 - 50, it is the median class.
Using Median formula,
Median $= l + \frac{h}{f} (\frac{N}{2} - C)$
$f_{1} + f_{2} = 79$
$46 = 40 + \frac{10}{65} [114.5 - (12 + 30 + f_{1})]$
$46 - 40 = (\frac{72.5 - f_{1}}{65}) \times 10$
$6 = (\frac{72.5 - f_{1}}{6.5})$
$f_{1} = 72.5 - 39 = 33.5 = 34$ ( $∵$ frequency is never a fraction)
$∴ f_{2} = 79 - 34 = 45$
$f_{1} + f_{2} = 79$

How to find missing frequency in medianFor exampleIf th

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SOLUTION

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