KVPY Sample Paper KVPY Stream-SX Model Paper-14

  • question_answer
    The variance of first 50 even natural numbers is:

    A) \[\frac{833}{4}\]

    B) 833

    C) 437

    D) \[\frac{437}{4}\]

    Correct Answer: B

    Solution :

    \[{{\sigma }^{2}}=\left( \frac{\sum{x_{i}^{2}}}{n} \right)-{{\overline{x}}^{2}}\] \[\overline{x}=\frac{\sum\limits_{r\,=\,1}^{50}{2r}}{50}=51\] \[{{\sigma }^{2}}=\frac{\sum\limits_{r\,=\,1}^{50}{4{{r}^{2}}}}{50}-{{(51)}^{2}}=833.\]


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