Question

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

You are given the median value is $46$ and the total number of items is $230$
Find:
Missing frequency

Answer 1

Variable	Frequaency	Cumulative frequency
$10-20$	$12$	$12$
$20-30$	$30$	$42$
$30-40$	$x$	$42+x$
$40-50$	$65$	$107+x$
$50-60$	$y$	$107+x+y$
$60-70$	$25$	$132+x+y$
$70-80$	$18$	$150+x+y$
	$N=230$

Given: Median$=46$

Then, median class$=40-50$

$l=40$,$h=50-40=10$,$f=65$,$F=42+x$

Median$=l+\frac{\frac{N}{2}-F}{f}\times h$

$\Rightarrow 46=40+\frac{115-(42+x)}{65}\times 10$

$\Rightarrow 46-40=\frac{115-(42+x)}{65}\times 10$

$\Rightarrow 6=\frac{73-x}{65}\times 10$

$\Rightarrow 390‬=730-10x$

$\Rightarrow 10x=730-390=340$

$\therefore x=\frac{340}{10}=34$

Given:$N=230$

$\Rightarrow 12+30+x+65+y+25+18=230$

$\Rightarrow 12+30+34+65+y+25+18=230$

$\Rightarrow y=230-184=46$

$\therefore x=34$ and $y=46$