A) \[\frac{\sqrt{{{a}^{2}}+{{b}^{2}}}}{2}\]
B) \[\frac{\left| a-b \right|}{2}\]
C) \[\left| a-b \right|\]
D) \[\frac{\sqrt{{{a}^{2}}+{{b}^{2}}}}{2}\]
Correct Answer: B
Solution :
\[\sigma =\sqrt{\frac{\sum{x_{i}^{2}}}{2}{{(\overline{x})}^{2}}}=\sqrt{\left( \frac{{{a}^{2}}+{{b}^{2}}}{2} \right)-{{\left( \frac{{{a}^{2}}+{{b}^{2}}}{2} \right)}^{2}}}\] \[=\sqrt{\frac{2{{a}^{2}}+2{{b}^{2}}-({{a}^{2}}+{{b}^{2}}+2ab)}{4}}=\frac{|a-b|}{2}\]
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