Question

If the mean of the following frequency distribution is $8$, find the value of ‘$p$’.

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

Answer 1

Step 1: Find the value of $fx$

$fx=x\times f$

$x$	$f$	$fx=x\times f$
$3$	$6$	$3\times 6=18$
$5$	$8$	$5\times 8=40$
$7$	$15$	$7\times 15=105$
$9$	$p$	$9\times p=9p$
$11$	$8$	$11\times 8=88$
$13$	$4$	$13\times 4=52$
	$N=41+p$	$\sum _{}fx=303+9p$

Step 2: Find the value of $p$.

$Mean(\overline{x)}$ $=\frac{{\displaystyle \sum _{}}fx}{N}$

$$\begin{gathered} \therefore 8=\frac{303+9p}{41+p} \\ \Rightarrow 303+9p=8\times (41+p) \\ \Rightarrow 303+9p=328+8p \\ \Rightarrow 9p-8p=328-303 \\ \Rightarrow p=25 \end{gathered}$$

Therefore, the value of $p=25$