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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    Find the value of p, if the mean of the following data is 20.
    \[{{x}_{i}}\] 15 17 19 20 +p 23
    \[{{f}_{i}}\] 2 3 4 5p 6

    A)  2                    

    B)         1                    

    C)  4                                

    D)  10      

    Correct Answer: B

    Solution :

    \[{{x}_{i}}\] \[{{f}_{i}}\] \[{{f}_{i}}{{x}_{i}}\]
    15 2 30
    17 3 51
    19 4 76
    \[20+p\] \[5\,p\] \[100p+5\,{{p}^{2}}\]
    23 6 138
    Total \[\Sigma {{f}_{i}}=15+5p\] \[\Sigma {{f}_{i}}{{x}_{i}}=295+100\,p+5\,{{p}^{2}}\]
    Mean \[=\frac{\Sigma {{f}_{i}}{{x}_{i}}}{\Sigma {{f}_{i}}}\Rightarrow 20=\frac{295+100p+5{{p}^{2}}}{15+15p}\] \[\Rightarrow \] \[20(15+5P)=295+100p+5{{p}^{2}}\] \[\Rightarrow \]\[300+100p=295+100p+5{{p}^{2}}\Rightarrow 5{{p}^{2}}=5\] \[\Rightarrow \] \[{{p}^{2}}=\pm 1\Rightarrow p=1\]           \[(\therefore \,\,p\ne -1)\]


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