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

  • question_answer
    Suppose a population A has 100 observations \[101,102,.....,200\] and another population B has 100 observations 151, 152 ???? 250. If \[{{V}_{A}}\,\,and\,\,{{V}_{B}}\] represent the variances of the two populations, respectively then \[\frac{{{V}_{A}}}{{{V}_{B}}}\] is

    A) 1

    B) \[\frac{9}{4}\]

    C) \[\frac{4}{9}\]

    D) \[\frac{2}{3}\]

    Correct Answer: A

    Solution :

    [a] \[\sigma _{x}^{2}=\frac{\sum{d_{i}^{2}}}{n}\] (Here deviations are taken from the mean). Since A and B both have 100 consecutive integers, therefore both have same standard deviation and hence the variance. \[\therefore \frac{{{V}_{A}}}{{{V}_{B}}}=1\] (As \[\sum{d_{i}^{2}}\] is same in both the cases)


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