10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    Find the weighted mean of first 'n' natural numbers, whose weights are proportional to the corresponding numbers.

    A)  \[\frac{2n+1}{3}\]     

    B)  \[\frac{4n+1}{3}\]         

    C)  \[\frac{{{n}^{2}}{{(n+1)}^{2}}}{2}\]          

    D)  \[\frac{(4n+1)(3n+1)}{7}\]

    Correct Answer: A

    Solution :

    (a): Weighted mean \[=\frac{1.1+2.2+3.3+.....(n-1)(n-1)+n.n}{n}=\frac{\sum\limits_{i=1}^{n}{{{n}^{2}}}}{n}\]                         


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