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KVPY Sample Paper KVPY Stream-SX Model Paper-3

  • question_answer
    5 students of a class have an average height 150 cm and variance \[18\text{ }c{{m}^{2}}\]. A new student, whose height is 156 cm, joined them. The variance \[(\text{in}\,\,\text{c}{{\text{m}}^{2}})\] of the height of these six students is:

    A) 22                                

    B) 20

    C) 16                                

    D) 18

    Correct Answer: B

    Solution :

    Combined variance\[=\frac{1}{{{n}_{1}}+{{n}_{2}}}\left( {{n}_{1}}\sigma _{1}^{2}+{{n}_{2}}\sigma _{2}^{2}+\frac{{{n}_{1}}{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}{{({{{\bar{x}}}_{1}}-{{{\bar{x}}}_{2}})}^{2}} \right)\]
    Put,      \[{{n}_{1}}=5,\]\[{{n}_{2}}=1,\]
                \[\sigma _{1}^{2}=18,\] \[\sigma _{2}^{2}=0\]
                \[{{\bar{x}}_{1}}=150,\] \[{{\bar{x}}_{2}}=156\]
    \[\therefore \]combined variance \[=\frac{1}{6}\left( 90+0+\frac{5}{6}(36) \right)=20\]


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