In a distribution of 10 observation, the sum of the observations is 60 and sum of their squares is 1000 , then the variance is

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Aicharya · Accepted Answer

Given, $n=10$, $\begin{aligned} & \Sigma x_i=60 \ & \Sigma x_i^2=1000\end{aligned}$ $\because \quad \operatorname{Mean}_{(\bar{X})}=\frac{\Sigma x_i}{n}=\frac{60}{10}=6$ Variance $=\frac{\Sigma\left(x_i-\bar{x}ight)^2}{n}$ $\begin{aligned} & =\frac{\Sigma x_i^2+\Sigma \bar{x}^2-2 \bar{x} \Sigma x_i}{n} \ & =\frac{1000}{10}+\frac{36 \cdot 10}{10}-\frac{2 	imes 6 	imes 60}{10} \ & =100+36-72 \ & =64\end{aligned}$

In a distribution of 10 observation, the sum of the observations is 60 and sum of their squares is 1000 ,…

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