Question

Find the value of $p$, if the mean of the following distribution is $7.5$.

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$x$	$3$	$5$	$7$	$9$	$11$	$13$
$f$	$6$	$8$	$15$	$p$	$8$	$4$	$41+p$
$fx$	$18$	$40$	$105$	$9p$	$88$	$52$	$303+9p$

We know, mean of a frequency distribution is calculated by:

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

Given mean $\overline{x}=7.5$.

$⟹$ $7.5=\frac{303+9p}{41+p}$

$⟹$$7.5\left(41+p\right)=303+9p$

$⟹$$307.5-303=9p-7.5p$

$⟹$$4.5=1.5p$

$⟹$$p=3$

Thus, option $C$ is correct.