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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    In an experiment with 15 observations on x, the following results were available. \[\Sigma {{x}^{2}}=2830,\Sigma x=170\] One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

    A) 78

    B) 188.66

    C) 177.33             

    D) 8.33

    Correct Answer: A

    Solution :

    [a]:\[n=15,\Sigma {{x}^{2}}=2830,\Sigma x=170\] (New)\[\Sigma {{x}^{2}}=2830-400+900=3330\] (New)\[\Sigma x=170-20+30=180\] Corrected variance, i.e., \[{{\sigma }^{2}}\] \[=\frac{(New)\Sigma {{x}^{2}}}{n}-{{\left( \frac{(New)\Sigma x}{n} \right)}^{2}}\] \[=\frac{3330}{15}-{{\left( \frac{180}{15} \right)}^{2}}=78.0\]


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