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

Step 1: Find the value of $fx$

$fx=x\times f$

$x$	$8$	$12$	$15$	$p$	$20$	$25$	$30$
$f$	$12$	$16$	$20$	$24$	$16$	$8$	$4$	$\sum _{}^{}f=100$
$fx$	$8\times 12=96$	$12\times 16=192$	$15\times 20=300$	$24\times p=24p$	$20\times 16=320$	$25\times 8=200$	$30\times 4=120$	$\sum _{}fx=1228+24p$

Step 2: Find the value of $p$.

$$\begin{gathered} Mean\left(\overline{x}\right)=\frac{{\displaystyle \sum }fx}{{\displaystyle \sum _{}f}} \\ \therefore 16.6=\frac{1228+24p}{100} \\ \Rightarrow 1228+24p=16.6\times 100 \\ \Rightarrow 1228+24p=1660 \\ \Rightarrow 24p=1660-1228 \\ \Rightarrow 24p=432 \\ \Rightarrow p=\frac{432}{24} \\ \Rightarrow p=18 \end{gathered}$$

Hence, the value of $p=18$.