A) 5
B) 10
C) 20
D) 40
Correct Answer: C
Solution :
\[\frac{1}{20}\sum\limits_{i=1}^{20}{({{x}_{i}}-\bar{x}}{{)}^{2}}=5\] \[\sum\limits_{i=1}^{20}{({{x}_{i}}-\bar{x}}{{)}^{2}}=100\] New, observations are,\[2{{x}_{1}},2{{x}_{2}},2{{x}_{3}},........2{{x}_{20}}\] Their mean, \[\bar{x}=\frac{2({{x}_{1}}+{{x}_{2}}+..........{{x}_{20}})}{20}=2\bar{x}\] Now, variance, \[\frac{1}{20}\sum\limits_{i=1}^{20}{{{(2{{x}_{i}}-2\bar{x})}^{2}}}=\frac{1}{20}\times 4\sum\limits_{i=1}^{20}{({{x}_{i}}-\bar{x}}{{)}^{2}}\] \[=\frac{1}{2}\times 4\times 100=20\]
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