Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is $24$.

Age in years	0-10	10-20	20-30	30-40	40-50
No. of persons	$5$	$25$	?	$18$	$7$

Answer 1

Let the missing frequency be $x$.

Age in years (x)	No. of persons (f)	C.F.
0-10	5	5
10-20	25	30
20-30	$x$	30 $+x$
30-40	18	48 $+x$
40-50	7	55 $+x$
	$N=55+x$

As, $N=55+x$ $\Rightarrow \frac{N}{2}=\frac{55+x}{2}$

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

As $median$ is given $24$, therefore median class is $20-30.$

Therefore,

$l=$lower limit of median class $=20$

$C=C.F.$ of the class preceding the median class $=30$

$h=$ higher limit - lower limit $=40-30=10$

$f=$frequency of median class $=x$

$\therefore median=20+\frac{\frac{55+x}{2}-30}{x}\times 10$

$24=20+\frac{x-5}{2x}\times 10$

$4=\frac{x-5}{x}\times 5$

$\Rightarrow 4x=5x-25$

$\Rightarrow x=25$

Hence, the missing frequency is $25.$