A) 437
B) \[\frac{437}{4}\]
C) \[\frac{833}{4}\]
D) \[833\]
Correct Answer: D
Solution :
[d] First 50 even natural numbers are 2, 4, 6?,100 Variance \[=\frac{\sum{x_{i}^{2}}}{N}-{{(\bar{x})}^{2}}\] \[\Rightarrow {{\sigma }^{2}}=\frac{{{2}^{2}}+{{4}^{2}}+...+{{100}^{2}}}{50}-{{\left( \frac{2+4+...+100}{50} \right)}^{2}}\] \[=\frac{4({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+...+{{50}^{2}})}{50}-{{(51)}^{2}}\] \[=4\left( \frac{50\times 51\times 101}{50\times 6} \right)-{{(51)}^{2}}=3434-2601\] \[\Rightarrow {{\sigma }^{2}}=833\]
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