2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Statistics

JEE Main & Advanced Mathematics Statistics Question Bank Self Evaluation Test - Statistics

  • question_answer
    The variance of the following distribution is
    \[{{x}_{i}}\] 2 3 11
    \[f({{x}_{i}})\] \[\frac{1}{3}\] \[\frac{1}{2}\] \[\frac{1}{6}\]

    A) 10

    B) 16

    C) 8

    D) 7.5

    Correct Answer: A

    Solution :

    [a] We construct the following table:
    \[{{x}_{i}}\] \[f({{x}_{i}})\] \[x_{i}^{2}\] \[f({{x}_{i}}).{{x}_{i}}\] \[f({{x}_{i}}).x_{_{i}}^{2}\]
    2 \[\frac{1}{3}\] 4 \[\frac{2}{3}\] \[\frac{4}{3}\]
    3 \[\frac{1}{2}\] 9 \[\frac{3}{2}\] \[\frac{9}{2}\]
    11 \[\frac{1}{6}\] 121 \[\frac{11}{6}\] \[\frac{121}{6}\]
    1 4 26
    \[\therefore \] Variance \[{{\sigma }^{2}}=\frac{\sum{f({{x}_{i}}).x_{i}^{2}}}{\sum{f({{x}_{i}})}}-{{\left( \frac{\sum{f({{x}_{i}}){{x}_{i}}}}{\sum{f({{x}_{i}})}} \right)}^{2}}\] \[=\frac{26}{1}-{{\left( \frac{4}{1} \right)}^{2}}=26-16=10\]


You need to login to perform this action.
You will be redirected in 3 sec spinner