If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_1^2=400$ and $\sum_{i=1}^n x_1=80$, then the least value of $n$ is

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Aicharya · Accepted Answer

Given, $\quad \sum_{i=1}^n x_i^2=400$ and $ \sum_{i=1}^n x_i=80 $ We know, $\frac{\Sigma\left(x_iight)^2}{n}-\left(\frac{\Sigma x_i}{n}ight)^2 \geq 0$ $ \begin{aligned} \Rightarrow & & \frac{400}{n}-\left(\frac{80}{n}ight)^2 & \geq 0 \ \Rightarrow & & 400 n & \geq 6400 \ \Rightarrow & & n & \geq 16 \ 	herefore & & n & =16 \end{aligned} $

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_1^2=400$ and $\sum_{i=1}^n x_1=80$…

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