If the mean of the following data is $20.6$ . Find the value of $p$ .
$x$ $10$ $15$ $p$ $25$ $35$
$f$ $3$ $10$ $25$ $7$ $5$

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Solution

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

$\Rightarrow$ mean = $\frac{(10 \times 3) + (15 \times 10) + (p \times 25) + (25 \times 7) + (35 \times 5)}{3 + 10 + 25 + 7 + 5}$

$\Rightarrow$ mean = $\frac{30 + 150 + 25 p + 175 + 175}{3 + 10 + 25 + 7 + 5} = 20.6$

$\Rightarrow 20.6 = \frac{1030 + 25 p}{50}$

$\Rightarrow 25 p = 500$

$\Rightarrow p = 20$

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Similar questions

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

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

18.75

p

$x_{i}$ :	$10$	$15$	$p$	$25$	$30$
$f_{i}$ :	$5$	$10$	$7$	$8$	$2$

21

p

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

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