If the median of the given data set is $16.5$ , what is $x$ ?

$15$ $16$ $18$ $13$ $11$

$x$ $20$ $12$ $22$ $23$

17

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18

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16

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20

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Solution

The correct option is A
$17$
Given data : $15, 16, 18, 13, 11, x, 20, 12, 22, 23$
Median : $16.6$

Ordered data : $11, 12, 13, 15, 16, x, 18, 20, 22, 23$
There are even number of points in data.
So, median $= 16.5 = \frac{16 + x}{2}$
$x + 16 = 33$
$\Rightarrow x = 17$

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$15$	$16$	$18$	$13$	$11$
$x$	$20$	$12$	$22$	$23$

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$16$	$15$	$19$	$18$	$13$

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