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In an experiment with 15 observations on $x$, we have $\sum x^2=2830, \sum x=170$. One observation that was 20 was found to be wrong and was replaced by the correct value 30 , then the corrected variance is
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78
$\begin{aligned} & \text { Correct variance }=\frac{\sum x^2-20^2+30^2}{15}-\left(\frac{\sum x-20+30}{15}\right)^2 \\ & =\frac{2830-400+90}{15}-\left(\frac{170-20+30}{15}\right)^2 \\ & =222-144=78\end{aligned}$
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