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JEE Main & Advanced AIEEE Solved Paper-2006

  • 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     AIEEE  Solved  Paper-2006

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

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

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

    D)        1

    Correct Answer: D

    Solution :

    Since, variance is independent of change of origin.   Thus,   variance   of   observations 101,102, ...,200 is  same  as  variance  of observations 151,152, ....250. \[\therefore \]  \[{{V}_{A}}={{V}_{B}}\] \[\Rightarrow \]               \[\frac{{{V}_{A}}}{{{V}_{B}}}=1\] NOTE Variance is independent of change of origin but not of scale.


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