If the mean of the following data is $20.2$ , find the value of $p$ .
$x$
$10$
$15$
$20$
$25$
$30$
$y$
$6$
$8$
$p$
$10$
$6$

11

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13

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15

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20

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Solution

The correct option is C $20$
Mean $\frac{\sum_{1}^{5} (x \times y)}{\sum_{1}^{5} y}$
$\Rightarrow 20.2 = \frac{60 + 120 + 20 p + 250 + 180}{6 + 8 + p + 10 + 6}$
$\Rightarrow (30 + p) \times 20.2 = 20 p + 610$
$\Rightarrow 0.2 p = 4$
$\Rightarrow p = 20$

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Similar questions

20.2

Observation	$10$	$15$	$20$	$25$	$30$
Frequency	$6$	$8$	m	$10$	$6$

Variable (x_i)	10	15	20	25	30
Frequency (f_i)	6	8	p	10	6

$x_{i}$	10	15	20	25	30
$f_{i}$	6	8	p	10	6

\begin{matrix} x & 10 & 15 & 20 & 25 & 30 f & 6 & 8 & p & 10 & 6 \end{matrix}

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p

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

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