$\begin {array} {1 1} (A)\;8.33 & \quad (B)\;78.00 \\ (C)\;188.66 & \quad (D)\;177.33 \end {array}$

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- $ \large\frac{1}{n}$$ \Sigma x^{2} - \bigg( \large\frac{1}{n}$$ \Sigma x \bigg)^2$

Given: $ \Sigma x = 170 \: \Sigma x^2 = 2830$ and increase in $ \Sigma x=10$

$\Rightarrow\: \Sigma x' = 170+10=180$

Increase in $ \Sigma x^2=900-400=500$

$\Rightarrow\: \Sigma x'^2=2830+500=3330$

Correct Variance = $ \large\frac{1}{n}$$ \Sigma x^{'2} - \bigg( \large\frac{1}{n}$$ \Sigma x' \bigg)^2$

$ = \large\frac{1}{15}$$ \times 3330 - \bigg( \large\frac{1}{15} $ $\times 180 \bigg)^2$

$ = 222-144$

$ = 78$

Ans : (B)

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