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JEE Main & Advanced Mathematics Statistics Question Bank Mean

  • question_answer
    If the mean of the numbers \[27+x\], \[31+x\], \[89+x\], \[107+x,\,156+x\] is 82, then the mean of \[130+x,\,126+x,\,68+x,\,50+x,\,1+x\] is                [Pb. CET 1989; Kurukshetra CEE 2000; Kerala (Engg.) 2001]

    A)                 75           

    B)                 157

    C)                 82           

    D)                 80

    Correct Answer: A

    Solution :

                       Given,                    \[82=\frac{(27+x)+(31+x)+(89+x)+(107+x)+(156+x)}{5}\]                    Þ \[82\times 5=410+5x\] Þ \[410-410=5x\] Þ \[x=0\]               \Required mean is,                    \[\bar{x}=\frac{130+x+126+x+68+x+50+x+1+x}{5}\]                                 \[\bar{x}=\frac{375+5x}{5}\]\[=\frac{375+0}{5}\]\[=\frac{375}{5}\]= 75.


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