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Find the value of $p$ if the Mean of the following distribution is $50$

$x$
$10$
$30$
$50$
$70$
$90$
$y$
$17$
$5 p + 3$
$32$
$7 p - 11$
$19$

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12

\frac{- 25}{2}

14

8

answer is B.

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Detailed Solution

Given data,

$x$	$10$	$30$	$50$	$70$	$90$
$y$	$17$	$5 p + 3$	$32$	$7 p - 11$	$19$

We know that mean is,

mean = \frac{\sum f_{i} x_{i}}{\sum f_{i}}

\Rightarrow mean = \frac{(10 \times 17 + 30 (5 p + 3) + 50 \times 32 + 70 (7 p - 1) + 90 \times 19)}{17 + 5 p + 3 + 32 + 7 p - 11 + 19}

\Rightarrow 50 = \frac{170 + 155 p + 90 + 1600 + 490 p - 70) + 1710}{60 + 15 p}

\Rightarrow 50 = \frac{170 + 155 p + 90 + 1600 + 490 p - 70 + 1710}{60 + 15 p}

\Rightarrow 50 (60 + 15 p) = 3500 + 640 p

\Rightarrow 3000 + 600 p = 3500 + 640 p

\Rightarrow 40 p = - 500

\Rightarrow p = - \frac{500}{40}

\Rightarrow p = - \frac{25}{2}

Thus, the value of p

= \frac{- 25}{2}

.
Hence, the correct option is 2.

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