If the total number of observations is $20, \sum x_i=1000$ and $\sum x_i^2=84000$, then the variance of the distribution is

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Aicharya · Accepted Answer

Given number of observation is 20 . $ \begin{aligned} & \mathrm{x}=20, \sum \mathrm{x}_{\mathrm{i}}=1000 	ext { and } \sum \mathrm{x}_{\mathrm{i}}^2=84000 \ & \sigma^2=\frac{1}{\mathrm{x}} \sum_{\mathrm{i}=1}^{\mathrm{x}}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}ight)^2 \ & =\frac{1}{\mathrm{x}} \sum_{\mathrm{i}=1}^{\mathrm{x}}\left(\mathrm{x}_1^2+\overline{\mathrm{x}}^2-2 \mathrm{x}_{\mathrm{i}} \overline{\mathrm{x}}ight) \ & \sigma^2=\frac{1}{\mathrm{x}} \sum \mathrm{x}_{\mathrm{i}}^2-\overline{\mathrm{x}}^2=\frac{1}{\mathrm{x}} \sum \mathrm{x}_{\mathrm{i}}^2-\left(\frac{1}{\mathrm{x}} \sum \mathrm{x}_{\mathrm{i}}ight)^2 \ & \sigma^2=\frac{1}{20} 	imes 84000-\left(\frac{1}{20} 	imes 1000ight)^2 \ & \sigma^2=4200-2500=1700 \end{aligned} $

If the total number of observations is $20, \sum x_i=1000$ and $\sum x_i^2=84000$, then the variance of the…

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