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In an experiment with 15 observations on $x$, the following results were available $\sum x^2=2830, \quad \sum x=170$. On 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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The correct answer is:
$78.00$
$\sum x=170, \sum x^2=2830$
Increase in $\sum x=10$, then $\sum x^{\prime}=170+10=180$
Increase in $\sum x^2=900-400=500$, then $\sum x^{\prime 2}=2830+500=3330$
$\therefore$ Variance $=\frac{1}{n} \sum x^{\prime 2}-\left(\frac{\sum x^{\prime}}{n}\right)^2$
$=\frac{3330}{15}-\left(\frac{180}{15}\right)^2=222-144=78$.
Increase in $\sum x=10$, then $\sum x^{\prime}=170+10=180$
Increase in $\sum x^2=900-400=500$, then $\sum x^{\prime 2}=2830+500=3330$
$\therefore$ Variance $=\frac{1}{n} \sum x^{\prime 2}-\left(\frac{\sum x^{\prime}}{n}\right)^2$
$=\frac{3330}{15}-\left(\frac{180}{15}\right)^2=222-144=78$.
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