The mean of following distribution is $6.5$ . Find the value of $k$ .
$x$ $2$ $4$ $6$ $8$ $10$
$f$ $5$ $3$ $7$ $6$ $k$

5

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4

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7

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8

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Solution

The correct option is B $7$
$x$ $f$ $f x$
$2$
$5$
$10$
$4$ $3$
$12$
$6$ $7$
$42$
$8$ $6$
$48$
$10$ $k$
$10 k$

Mean $= \frac{\sum f x}{\sum f} = 6.5$
$=> \frac{10 + 12 + 42 + 48 + 10 k}{5 + 3 + 7 + 6 + k} = 6.5$
$=> \frac{112 + 10 k}{21 + k} = 6.5$
$=> 112 + 10 k = 136.5 + 6.5 k$
$=> 3.5 k = 24.5$
$=> k = 7$

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$f r e q u e n c y = f$	$4$	$7$	$10$	$16$	$k$	$3$

If the mean of the following frequency distribution is $7.2$ find value of $k$ .

$\begin{matrix} x & 2 & 4 & 6 & 8 & 10 & 12 f & 4 & 7 & 10 & 16 & k & 3 \end{matrix}$

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$x$	$3$	$5$	$7$	$9$	$11$	$13$
$f$	$6$	$8$	$15$	$p$	$8$	$4$

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$f$	$4$	$6$	$8$	$12$	$17$	$11$	$7$	$6$	$5$	$3$

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