Attempt the missing value of the variate for the following distributed whose mean is $31.87$ .
$x$ $12$
$20$ $27$ $33$ $-$ $54$
$f$ $8$ $16$ $48$ $90$ $30$ $8$

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Solution

$\Rightarrow$ Let missing variate be $x_{1}$ .
$x$ $f$ $f x$
$12$ $8$ $96$
$20$ $16$ $320$
$27$ $48$ $1296$
$33$ $90$ $2970$
$x_{1}$ $30$ $30 x_{1}$
$54$ $8$ $432$
$\sum f = 200$ $\sum f x = 5114 + 30 x_{1}$
$\Rightarrow$ $M e a n = \frac{\sum f x}{\sum f}$

$\Rightarrow$ $31.87 = \frac{5114 + 30 x_{1}}{200}$

$\Rightarrow$ $6374 = 5114 + 30 x_{1}$
$\Rightarrow$ $1260 = 30 x_{1}$
$∴$ $x_{1} = 42$

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x:	8	12	15	p	20	25	30
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Find the missing value of $p$ for the following distribution whose mean is 12.58.

$\begin{matrix} x : & 5 & 8 & 10 & 12 & p & 20 & 25 f : & 2 & 5 & 8 & 22 & 7 & 4 & 2 \end{matrix}$

x	8	12	15	p	20	25	30
f	12	16	20	24	16	8	4

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