A) \[\frac{1}{n}\]
B) \[\sqrt{2}\]
C) \[2\]
D) \[\frac{\sqrt{2}}{n}\]
Correct Answer: C
Solution :
If corresponding frequency of each observations are\[{{f}_{1}},{{f}_{2}},....{{f}_{n}},\]then \[\sigma =\frac{\sqrt{\sum\limits_{i=1}^{n}{{{({{x}_{1}}-\overline{x})}^{2}}}}}{N}\] In the 2n observations, half of them equal to a and remaining half equal to\[-\text{ }a\]. Then, the mean of total n observations is equal to zero. \[\therefore \] \[SD=\sqrt{\frac{\Sigma {{(x-\overline{x})}^{2}}}{N}}\] \[\Rightarrow \]\[2=\sqrt{\frac{\Sigma {{x}^{2}}}{2n}}\] \[\Rightarrow \]\[4=\frac{\Sigma {{x}^{2}}}{2n}\]\[\Rightarrow \]\[4=\frac{2n{{a}^{2}}}{2n}\] \[\Rightarrow \] \[{{a}^{2}}=4\] \[\therefore \] \[|a|=2\]
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