In an experiment with 15 observations for $x$, the following results were available $\sum x^2=2830, \sum x=170$. One observation 20 was found to be wrong and was replaced by the correct value 30 . Then the corrected variance is

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Aicharya · Accepted Answer

Given: $\sum x=170$ and $\sum x^2=2830$ Corrected sum $\begin{aligned} & \sum x=170-20+30=180 \ & \sum x^2=2830-400+900=3330 \end{aligned}$ $	herefore \quad$ Corrected variance $\begin{aligned} & =\left(\frac{\sum x^2}{n}ight)-\left(\frac{\sum x}{n}ight)^2 \ & =\left(\frac{3330}{15}ight)-\left(\frac{180}{15}ight)^2 \ & =222-144=78 \end{aligned}$

In an experiment with 15 observations for $x$, the following results were available $\sum x^2=2830, \sum…

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