KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    If mean and standard deviation of 5 observations \[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}},{{x}_{5}}\] are 10 and 3, respectively, then the variance of 6 observations \[{{x}_{1}},{{x}_{2}},.....{{x}_{3}}\] and \[-50\] is equal to:

    A) \[509.5\]

    B) \[586.5\]

    C) \[582.5\]      

    D) \[507.5\]

    Correct Answer: D

    Solution :

    \[{{(3)}^{2}}=\frac{1}{5}\left( e{{x}^{2}}-\frac{{{(ex)}^{2}}}{5} \right)\]
    \[9=\frac{1}{5}\left( \sum{{{x}^{2}}-\frac{2500}{5}} \right)\]
    \[\therefore \]      \[\sum{{{x}^{2}}=545}\]
    New variable\[=\frac{1}{6}\left( 3045-\frac{0}{6} \right)=507.5\]

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