If M and ${(σ)}^{2}$ represents respectively the mean deviation from the mean and the variance for the data 1,3,5,7,11,13,17,19,23 then $3 (σ^{2} - M) =$

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232

112

224

136

answer is D.

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Detailed Solution

$M = \frac{\sum | x i - \bar{x} |}{n}; \bar{x} = 11$
$M = \frac{56}{9}$ variance $(σ^{2}) = \frac{\sum {| x_{i} - \bar{x} |}^{2}}{η}$
$σ^{2} = \frac{464}{9} 3 (σ^{2} - M) = 3 (\frac{464}{9} - \frac{56}{9}) \Rightarrow 136$

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