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13.Statistics
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If $x_1, x_2,.....x_n$ are $n$ observations such that $\sum\limits_{i = 1}^n {x_i^2} = 400$ and $\sum\limits_{i = 1}^n {{x_i}} = 100$ , then possible value of $n$ among the following is
A
$18$
B
$20$
C
$24$
D
$27$
Solution
Use $: \sigma^{2} \geq 0$
$ \Rightarrow \frac{\sum x_{i}^{2}}{n}-\left(\frac{\sum x_{i}}{n}\right)^{2} \geq 0$
$\Rightarrow \quad \frac{400}{n}-\frac{10000}{n^{2}} \geq 0 $
$\Rightarrow n \geq 25$
Standard 11
Mathematics