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

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

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Solution

The correct option is C 15
$\begin{matrix} x_{i} & f_{i} & x_{i} \times f_{i} 5 & 2 & 10 8 & 5 & 40 10 & 8 & 80 12 & 22 & 264 p & 7 & 7 p 20 & 4 & 80 25 & 2 & 50 T o t a l & 50 & 524 + 7 p \end{matrix}$

$∴ M e a n (¯ x) = \frac{\sum f_{i} x_{i}}{\sum f_{i}} \Rightarrow 12.58 = \frac{524 + 7 p}{50} \Rightarrow 629 = 524 + 7 p \Rightarrow 7 p = 105 \Rightarrow p = 15$

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Similar questions

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

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

12.58

$x_{i}$	5	8	10	12	P	20	25
$f_{i}$	2	5	8	22	7	4	2

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

12.58

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

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