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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    If \[{{x}_{i}}'s\] are the mid-point of the class intervals of grouped data, \[{{f}_{i}}'s\] are the corresponding frequencies and \[\overline{x}\] is the mean, then \[\sum{\left( {{f}_{i}}{{x}_{i}}-\overline{x} \right)}\] is equal to 

    A)  0      

    B)  - 1              

    C)  1                                

    D)  2

    Correct Answer: A

    Solution :

    (a): \[\overline{X}=\frac{\sum{{{f}_{i}}{{x}_{i}}}}{n}\] \[\sum{\left( {{f}_{i}}{{x}_{i}}-\overline{x} \right)}=\sum{{{f}_{i}}{{x}_{i}}-\sum{\overline{x}}}\] \[=n\overline{x}-n\overline{x}\]= 0                    


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