10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    If \[{{x}_{1}},{{x}_{2}},.......,{{x}_{n}}\] are 'n' observations such that \[\sum\limits_{1}^{n}{\left( {{x}_{1}}+5 \right)=200}\] and \[\sum\limits_{1}^{n}{\left( {{x}_{1}}+9 \right)=400}\]; then find 'n'.

    A)  30                               

    B)  50     

    C)  70                               

    D)  90

    Correct Answer: B

    Solution :

    (b): \[\sum\limits_{1}^{n}{\left( {{x}_{i}}+5 \right)=\sum\limits_{1}^{n}{{{x}_{i}}+5n=200}}\]???(1) \[\sum\limits_{i=1}^{n}{\left( {{x}_{i}}+9 \right)=\sum\limits_{1}^{n}{{{x}_{i}}+9n=400}}\]?????(2) Subtracting (2) ? (1) \[\Rightarrow \]4n = 200 \[\Rightarrow \]n = 50     


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