If x₁, x₂,.....xₙ are n observations such that Σlimits_{i = 1}^n {xᵢ^2} = 400 and Σl

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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

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