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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    Candidates of four school appear in a mathematics test. The data is as follows:
    Schools No. of Candidates Average Score
    I. 60 75
    II. 48 80
    III. Not available 55
    IV. 40 50
    If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.

    A)  51                              

    B)  52                              

    C)         50                  

    D)         53

    Correct Answer: B

    Solution :

    Let the number of candidates that appeared from school ill-be x.
    School Average \[{{x}_{i}}\] Number of Candidates \[({{f}_{i}})\] \[{{f}_{i}}{{x}_{i}}\]
    I 75 60 4500
    II 80 48 3840
    III 55 x 55 x
    IV 50 40 2000
    \[\Sigma {{f}_{i}}=148+x\] \[\Sigma {{f}_{i}}{{x}_{i}}=10340+55x\]
    Average score of the candidates of all the four schools \[=\frac{\Sigma {{f}_{i}}{{x}_{i}}}{\Sigma {{f}_{i}}}\,\,\,\Rightarrow \,\,\,\,66=\frac{10349+55x}{148+x}\] \[\Rightarrow \]            \[9768+66\,x=10340+55\,x\] \[\Rightarrow \]            \[11\,x=572\,\,\Rightarrow \,\,x=52\]


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