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Q.
Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations such that $\Sigma x_{i}^{2}=400$ and $\Sigma x_{ i }=80$. Then a possible value of $n$ among the following is
Statistics
Solution:
Since root mean square $\geq$ arithmetic mean
$\sqrt{\frac{\displaystyle\sum_{i=1}^{n} x_{i}^{2}}{n}} \geq \frac{\displaystyle\sum_{i=1}^{n} x_{i}}{n}$
$=\sqrt{\frac{400}{n}} \geq \frac{80}{n}$
$\Rightarrow n \geq 16$
Hence, the possible value of $n$ is $18$