A) 74.92
B) 37.98
C) 38.98
D) None of these
Correct Answer: A
Solution :
We know that variance of n natural numbers is \[=\frac{1}{n}\sum\limits_{i=1}^{n}{x_{i}^{2}}-{{\left( \frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}} \right)}^{2}}\] Variance \[({{\sigma }^{2}})=\frac{1}{30}[{{1}^{2}}+{{2}^{2}}+...+{{30}^{2}}]\] \[=\frac{1}{30}\times \frac{30\times 31\times (2\times 30+1)}{6}-{{\left[ \frac{1}{30}\times \frac{30\times 31}{2} \right]}^{2}}\] \[=\frac{30\times 61}{6}-\frac{31\times 31}{4}\] \[=\frac{31\times 2\times 61-31\times 3\times 31}{12}\] \[=\frac{31}{12}[122-93]=\frac{31\times 29}{12}\] \[=\frac{899}{12}=74.916\] \[=74.92\]
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