If the mean of the following data is $15$ , find $p$ .
$x$ : $5$ $10$ $15$ $20$ $25$
$f$ : $6$ $p$ $6$ $10$ $5$

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Solution

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

$\Rightarrow$ mean = $\frac{(5 \times 6) + (10 \times p) + (15 \times 6) + (20 \times 10) + (25 \times 5)}{6 + p + 6 + 10 + 5}$

$\Rightarrow$ mean = $\frac{30 + 10 p + 90 + 200 + 125}{27 + p} = 15$

$\Rightarrow 405 + 15 p = 445 + 10 p$

$\Rightarrow 5 p = 40$

$\Rightarrow p = 8$

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Similar questions

x:	5	10	15	20	25
f:	6	p	6	10	5

x:	5	10	15	20	25
f:	6	p	6	10	5

20.2

p

$x$	$10$	$15$	$20$	$25$	$30$
$y$	$6$	$8$	$p$	$10$	$6$

21

p

$x$	$10$	$15$	$20$	$25$	$35$
$f$	$6$	$10$	$p$	$10$	$8$

x:	10	15	p	25	35
f:	3	10	25	7	5

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