Question

Find the missing frequency ‘$p$’ for the following frequency distribution whose mean is $28.25$.

$x$	$15$	$20$	$25$	$30$	$35$	$40$
$f$	$8$	$7$	$p$	$14$	$15$	$6$

Answer 1

Step 1: Find the values of $fx$

$fx=x\times f$

$x$	$f$	$fx=x\times f$
$15$	$8$	$15\times 8=120$
$20$	$7$	$20\times 7=140$
$25$	$p$	$25\times p=25p$
$30$	$14$	$30\times 14=420$
$35$	$15$	$35\times 15=525$
$40$	$6$	$40\times 6=240$
	$N=50+P$	$\sum _{}fx=1445+25p$

Step 2: Find the value of $p$.

$Mean=\frac{{\displaystyle \sum _{}fx}}{N}$

$$\begin{gathered} \therefore 28.25=\frac{1445+25p}{50+p} \\ \Rightarrow 1445+25p=28.25\times (50+p) \\ \Rightarrow 1445+25p=1412.5+28.25p \\ \Rightarrow 28.25p-25p=1445-1412.5 \\ \Rightarrow 3.25p=32.5 \\ \Rightarrow p=10 \end{gathered}$$

Therefore, the value of $p=10$.