A) \[\frac{\sqrt{{{a}^{2}}+{{b}^{2}}}}{2}\]
B) \[|a-b|\]
C) \[\frac{\left| a-b \right|}{2}\]
D) \[\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{2}}\]
Correct Answer: C
Solution :
[c] \[\sigma =\sqrt{\frac{\Sigma x_{1}^{2}}{2}-{{(\bar{x})}^{2}}}=\sqrt{\left( \frac{{{a}^{2}}+{{b}^{2}}}{2} \right)-{{\left( \frac{a+b}{2} \right)}^{2}}}\] \[=\sqrt{\frac{2{{a}^{2}}+2{{b}^{2}}-({{a}^{2}}+{{b}^{2}}+2ab)}{4}}=\frac{|a-b|}{2}\]
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