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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • 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)  80.33                                   

    B)  78.00

    C)  188.66                                 

    D)  177.33

    Correct Answer: B

    Solution :

                    Corrected value \[\Sigma x=170-20+30=180\] and \[\Sigma {{x}^{2}}=2830-{{(20)}^{2}}+{{(30)}^{2}}=3330\] \[\therefore \]Corrected variance \[=\frac{\Sigma {{x}^{2}}}{n}-{{\left( \frac{\Sigma x}{n} \right)}^{2}}\]                                 \[=\frac{3330}{15}-{{\left( \frac{180}{15} \right)}^{2}}\]                                 \[=222-144=78\]


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