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VIT Engineering VIT Engineering Solved Paper-2008

  • question_answer
    Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25) 8      12      13    15    22 are

    A)  14, 4.604      

    B)  15, 4.604

    C)  14, 5.604      

    D)  None of these

    Correct Answer: A

    Solution :

    \[\overline{x}=\frac{8+12+13+15+22}{5}=\frac{70}{5}=14\]
    \[x\] \[(x-\bar{x})\] \[{{(x-\bar{x})}^{2}}\]
    8 \[-\]6 36
    12 \[-\]2 4
    13 \[-\]1 1
    15 +1 1
    22 +8 64
    \[\Sigma \,x=70\] \[\Sigma \,(x-\bar{x})=0\] \[\Sigma \,{{x}^{2}}=106\]
    \[\therefore \]\[\sigma =\sqrt{\frac{\Sigma {{(x-\bar{x})}^{2}}}{N}}\]         \[=\sqrt{\frac{106}{5}}=\sqrt{21.2}\]         \[=4.604\]


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