Question

The mean of the following frequency distribution is $21\frac{1}{7}$. Find the value of $f$

C.I	0-10	10-20	20-30	30-40	40-50
$f$	$8$	$22$	$31$	$f$	$2$

Answer 1

$\Rightarrow$ $\overline{x}=21\frac{1}{2}=\frac{148}{7}$ [ Given ]

$C.I$	$f_i$	$x_i$	$f_i{x}_i$
$0-10$	$8$	$5$	$40$
$10-20$	$22$	$15$	$330$
$20-30$	$31$	$25$	$775$
$30-40$	$f$	$35$	$35f$
$40-50$	$2$	$45$	$90$
	$\sum f_i=63+f$		$\sum f_i{x}_i=1235+35f$

$\Rightarrow$ $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

$\Rightarrow$ $\frac{148}{7}=\frac{1235+35f}{63+f}$

$\Rightarrow$ $148(63+f)=7(1235+35f)$

$\Rightarrow$ $9324+148f=8645+245f$

$\Rightarrow$ $97f=679$

$\therefore$ $f=7$