A) 9
B) 4
C) 3
D) 2
Correct Answer: D
Solution :
[d] Let \[\sum\limits_{i=1}^{9}{({{x}_{i}}-5)}=9\Rightarrow \sum\limits_{i=1}^{9}{{{x}_{i}}-\sum\limits_{i=1}^{9}{5=9}}\] \[\Rightarrow \sum\limits_{i=1}^{9}{{{x}_{i}}-(9\times 5)=9;}\] \[\sum{{{x}_{i}}-45=\Rightarrow \sum{{{x}_{i}}=54}}\] Similarly, \[\sum{x_{i}^{2}-10\times 54+25\times 9=45\Rightarrow \sum{x_{i}^{2}=360}}\] \[\Rightarrow \sigma =\sqrt{\frac{360}{9}-{{\left( \frac{54}{9} \right)}^{2}}}=\sqrt{\frac{324}{81}}=2\]
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