Question

Find the missing frequency ($p$) for the following distribution whose mean is $7.68$

$x$:	$3$	$5$	$7$	$9$	$11$	$13$
$f$:	$6$	$8$	$15$	$p$	$8$	$4$

Answer 1

Mean =$\frac{\sum x_i{f}_i}{\sum f_i}$

$\Rightarrow$mean =$\frac{(3\times 6)+(5\times 8)+(7\times 15)+(9\times p)+(11\times 8)+(13\times 4)}{8+6+15+p+8+4}$

$\Rightarrow$mean =$\frac{18+40+105+9p+88+52}{8+6+15+p+8+4}=7.68$

$\Rightarrow 314.88+7.68p=303+9p$

$\Rightarrow 11.88=1.32p$

$\Rightarrow p=9$