Find the missing frequency p for the following frequency distribu… - Vidyadip

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

We prepare the follwoing frequency distribution table:

$(x_i)$	$(f_i)$	$f_ix_i$
$15$	$8$	$120$
$20$	$7$	$140$
$25$	$p$	$25p$
$30$	$14$	$420$
$35$	$15$	$525$
$40$	$6$	$240$
	$\sum\text{f}_\text{i}=50+\text{p}$	$\sum\text{f}_\text{i}\text{x}_\text{i}=14145+25\text{p}$

Mean $=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}=\frac{1445+25\text{p}}{50+\text{p}}=28.25$
$\therefore\ \frac{1445+25\text{p}}{50+\text{p}}=28.25$
$\Rightarrow1445+25\text{p}=(28.25)(50+\text{p})$
$\Rightarrow1445+25\text{p}=1412.50+28.25\text{p}$
$\Rightarrow-28.25\text{p}+25\text{p}=-1445+1412.50$
$\Rightarrow-3.25\text{p}=-32.5$
$\Rightarrow\text{p}=\frac{32.5}{3.25}=10$
$\therefore\ $the value of $p = 10$

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