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Let $x_1, x_2, \ldots, x_n$ be $n$ observations such that $\sum x_i^2=400$ and $\sum x_i=80$. Then a possible value of $n$ among the following is
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The correct answer is:
$18$
Since, root mean square $\geq$ arithmetic mean
$\therefore \sqrt{\frac{\sum_{i=1}^n x_i^2}{n}} \geq \frac{\sum_{i=1}^n x_i}{n}=\sqrt{\frac{400}{n}} \geq \frac{80}{n} \Rightarrow n \geq 16$
Hence, possible value of $n=18$.
$\therefore \sqrt{\frac{\sum_{i=1}^n x_i^2}{n}} \geq \frac{\sum_{i=1}^n x_i}{n}=\sqrt{\frac{400}{n}} \geq \frac{80}{n} \Rightarrow n \geq 16$
Hence, possible value of $n=18$.
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