Find the missing frequency (p) for the following distribution who…

Question

Find the missing frequency $(p)$ for the following distribution whose mean is $7.68$

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

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Answer

Calculation of mean:

$x_i$	$f_i$	$x_if_i$
$3$	$6$	$18$
$5$	$8$	$40$
$7$	$15$	$105$
$9$	$p$	$9p$
$11$	$8$	$88$
$13$	$4$	$52$
Total	$\sum\text{f}_\text{i}=41+\text{p}$	$\sum\text{f}_\text{i}\text{x}_\text{i}=303+9\text{p}$

We have,
$\sum\text{f}_\text{i}=41+\text{p},\sum\text{f}_\text{i}\text{x}_\text{i}=303+9\text{p}$ $\therefore\text{Mean}=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}$
$\Rightarrow7.68=\frac{303+9\text{p}}{41+\text{p}}$
$\Rightarrow303 + 9\text{p} = 314.88 + 7.68\text{p}$
$\Rightarrow1.32\text{p} = 314.88 - 303$
$\Rightarrow\text{p}=\frac{11.88}{1.32}$
$\Rightarrow\text{p} = 9$

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