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Mean

If the mean d...

Question

If the mean deviation about the median of the numbers $k, 3 k, 7 k, 9 k, 11 k, 13 k$ is $11,$ then $k$ is equal to $(k > 0)$

\frac{5}{3}

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\frac{22}{7}

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3

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6

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Solution

The correct option is C $3$
Median $= \frac{7 k + 9 k}{2} = 8 k$
Also, mean deviation about median $= 11$
$\Rightarrow \frac{\sum | x_{i} - 8 k |}{6} = 11$
$\Rightarrow 7 k + 5 k + k + k + 3 k + 5 k = 66$
$\Rightarrow 22 k = 66$
$∴ k = 3$

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