JEE Main & Advanced Mathematics Statistics Question Bank Mean

  • question_answer
    The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is   [AMU 1992; DCE 1996]

    A)                 \[\frac{1}{5}\]        

    B)                 \[\frac{15}{4}\]

    C)                 4             

    D)                 8

    Correct Answer: B

    Solution :

               \[\frac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{10}}}{10}=4.5\]                    Þ \[{{x}_{1}}+{{x}_{2}}+.....+{{x}_{10}}=45\]                    and  \[\frac{{{x}_{11}}+{{x}_{12}}+.....+{{x}_{40}}}{30}=3.5\]                    Þ \[{{x}_{11}}+{{x}_{12}}+.....+{{x}_{40}}=105\]                    \\[{{x}_{1}}+{{x}_{2}}+.....+{{x}_{40}}=150\]                                 \ \[\frac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{40}}}{40}=\frac{150}{40}\]\[=\frac{15}{4}\].


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