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JEE Main & Advanced Sample Paper JEE Main Sample Paper-40

  • question_answer
    Let \[{{\overline{X}}_{1}}\]and\[{{\overline{X}}_{2}}\] means of two distributions such that \[{{\overline{X}}_{1}}<{{\overline{X}}_{2}}\]and \[\overline{X}\]is the mean of the combined distribution.
    Statement-1   :   \[{{\overline{X}}_{1}}<\overline{X}<{{\overline{X}}_{2}}\]
    Statement-2:      \[\overline{X}=\frac{{{\overline{X}}_{1}}+{{\overline{X}}_{2}}}{2}\]

    A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

    B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

    C) Statement-1 is true, Statement-2 is false.

    D) Statement-1 is false, Statement-2 is true.

    Correct Answer: D

    Solution :

    If \[{{n}_{1}}\] and \[{{n}_{2}}\] are the numbers of items in the two distributions then \[\overline{X}=\frac{{{n}_{1}}{{\overline{X}}_{1}}+{{n}_{2}}{{\overline{X}}_{2}}}{{{n}_{1}}+{{n}_{2}}}\]


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