A set F, which contains the elements $4, 5, 11, 13, 16, 18,$ and x. If both the median and average(arithmetic mean) of Set F equal $11$ , what must be the value of x?

9

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10

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11

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12

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Solution

The correct option is B $10$
Given, set $f = 4, 5, 11, 13, 16, 18, x$
Average of set $F = 11$
$\Rightarrow \frac{4 + 5 + 11 + 13 + 16 + 18 + x}{7} = 11$
$\Rightarrow \frac{67 + x}{7} = 11$
$\Rightarrow 67 + x = 77$
$\Rightarrow x = 77 - 67 = 10$

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