Let x_1,x_2,.........,x_{100} are 100 observa | vedclass

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Question

$\bar{x}=\frac{\sum x_{i}}{100}=0$  and 

$\frac{\sum\left|x_{i}-\bar{x}\right|}{100}=5 \Rightarrow \sum\left|x_{i}\right|=500$

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Vedclass · Accepted Answer

$30$

Vedclass · Answer

$\bar{x}=\frac{\sum x_{i}}{100}=0$  and 

$\frac{\sum\left|x_{i}-\bar{x}\right|}{100}=5 \Rightarrow \sum\left|x_{i}\right|=500$

$ \Rightarrow \sum {x_i^2}  + 2\sum\limits_{1 \le i < j \le 100} {\left| {{x_i}{x_j}} \right|}  = {(500)^2}$

$\Rightarrow \frac{\sum x_{i}^{2}}{100}=\frac{(500)^{2}-2 \sum\left|x_{i} x_{j}\right|}{100}=2500-1600$

$S. D.=\sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{100}}=\sqrt{900}=30$

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Let $x_1,x_2,.........,x_{100}$ are $100$ observations such that $\sum {{x_i} = 0,\,\sum\limits_{1 \leqslant i \leqslant j \leqslant 100} {\left| {{x_i}{x_j}} \right|} } = 80000\,\& $ mean deviation from their mean is $5,$ then their standard deviation, is-

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