Question

Find the value of $p$ for the following distribution whose mean is $16.6$.

$x$:	$8$	$12$	$15$	$p$	$20$	$25$	$30$
$f$:	$12$	$16$	$20$	$24$	$16$	$8$	$4$

Answer 1

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

$\Rightarrow$mean =$\frac{(8\times 12)+(12\times 16)+(15\times 20)+(p\times 24)+(20\times 16)+(25\times 8)+(30\times 4)}{12+16+20+24+16+8+4}$

$\Rightarrow$mean =$\frac{96+192+300+24p+320+200+120}{12+16+20+84+16+8+4}=16.6$

$\Rightarrow 1660=1228+24p$

$\Rightarrow 24p=432$

$\Rightarrow p=18$