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The mean and standard deviatoin of 10 observations are 20 and 8 respectively later on it was observed that one observation was recorded as 50 instad of 40 then correct variance is

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Detailed Solution

old $\bar{x} = \frac{ε x_{i}}{η} \Rightarrow 20 = \frac{ε x_{i}}{10} \Rightarrow ε x_{i} = 200$
$σ = 8 = \sqrt{\frac{ε {x_{i}}^{2}}{10} - {(20)}^{2}} \Rightarrow ε {x_{i}}^{2} = 4640$

New $ε x_{i} = 190$

$ε {x_{i}}^{2} = 4640 + 40^{2} - 50^{2} = 3740$

$ε \frac{1}{10} \times 3740 - {(l 9)}^{2} = 13$

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