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Median for Grouped Data

An incomplete...

Question

An incomplete frequency distribution is given below Median value is $46$ , the missing frequency is
Variate Frequency
$10 - 20$ $12$
$20 - 30$ $30$
$30 - 40$ ?
$40 - 50$ $65$
$50 - 60$ $45$
$60 - 70$ $25$
$70 - 80$ $18$
Total $229$

33

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35

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34

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26

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Solution

The correct option is A $34$
Given Median $= 46$ , which lies in $40 - 50$ class
$Median = l + h \frac{{\frac{N}{2} - C}}{f}$
where $f =$ freq. of median class
$C =$ cumulative freq.of the class preceding the median class.

$∴ 46 = 40 + 10 \frac{[\frac{229}{2} - (x + 42)]}{65}$

where, $x =$ freq.of class $30 - 40$
$\Rightarrow x = 33.5 = 34$

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Similar questions

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

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

46

230.

46

230

f_{1}

f_{2}

46

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

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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