11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer 17) The variance of n natural is

    A) \[\frac{{{n}^{2}}+1}{12}\]                 

    B) \[\frac{\left( n+1 \right)\left( 2n+1 \right)}{6}\]

    C) \[\frac{{{n}^{2}}-1}{12}\]  

    D)        None of these

    Correct Answer: C

    Solution :

    [c] Variance\[={{\sigma }^{2}}={{(S.D.)}^{2}}\] \[=\frac{\sum{f.{{d}^{2}}}}{N}-{{\left( \frac{\sum{fd}}{N} \right)}^{2}}=\frac{(n-1)\left( 2n+1 \right)}{6}+{{\left( \frac{n+1}{2} \right)}^{2}}\] \[=\frac{2(2{{n}^{2}}+3n+1)-3({{n}^{2}}+2n+1)}{12}=\frac{{{n}^{2}}-1}{12}\] Hence, option [c] is correct.                        

adversite



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