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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