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.
class interval
10-20
20-30
30-40
40-50 50-60 60-70 70-80
Frequency 12 30 $f_{1}$ 65 $f_{2}$ 25 18

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Solution

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

Suggest Corrections

122

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46

46

230

f_{1}

f_{2}

46

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$12$	$30$	$f_{1}$	$65$	$f_{2}$	$25$	$18$	$229$

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$-$	$65$	$-$	$25$	$18$

46

230.

An Incomplete distribution is given below:

Variables	10−20	20−30	30−40	40−50	50−60	60−70	70−80	Total
Frequency	12	30	?	65	?	25	18	229

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class interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	12	30	$f_{1}$	65	$f_{2}$	25	18