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In an experiment with 15 observations on $x$, the following results were available: $\Sigma x^2=2830, \Sigma x=170$ One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected variance is
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$78.00$
$78.00$
$\Sigma x=170, \Sigma x^2=2830$ increase in $\Sigma x=10$, then
$\Sigma x^{\prime}=170+10=180$
Increase in $\Sigma \mathrm{x}^2=900-400=500$ then
$\Sigma x^{\prime 2}=2830+500=3330$
Variance $=\frac{1}{n} \Sigma x^{\prime 2}-\left(\frac{1}{n} \Sigma x^{\prime}\right)^2$
$=\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2=222-144=78$
$\Sigma x^{\prime}=170+10=180$
Increase in $\Sigma \mathrm{x}^2=900-400=500$ then
$\Sigma x^{\prime 2}=2830+500=3330$
Variance $=\frac{1}{n} \Sigma x^{\prime 2}-\left(\frac{1}{n} \Sigma x^{\prime}\right)^2$
$=\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2=222-144=78$
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