Find the missing value of $p$ for the following distribution whose mean is $12.58$ .
$x$ : $5$ $8$ $10$ $12$ $p$ $20$ $25$
$f$ : $2$ $5$ $8$ $22$ $7$ $4$ $2$

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Solution

Mean = $\frac{\sum x_{i} f_{i}}{\sum f_{i}}$

$\Rightarrow$ mean = $\frac{(5 \times 2) + (8 \times 5) + (10 \times 8) + (12 \times 22) + (p \times 7) + (20 \times 4) + (25 \times 2)}{2 + 5 + 8 + 22 + 7 + 4 + 2}$

$\Rightarrow$ mean = $\frac{10 + 40 + 80 + 264 + 7 p + 80 + 50}{2 + 5 + 8 + 22 + 7 + 4 + 2} = 12.58$

$\Rightarrow \frac{629 + 7 p}{50} = 12.58$

$\Rightarrow 7 p = 105$

$\Rightarrow p = 15$

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Similar questions

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:	5	8	10	12	p	20	25
f:	2	5	8	22	7	4	2

Find the missing value of p for the following distribution whose mean is 12.58.

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

p

16.6

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

p

7.68

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

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