5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance of the height of these six students is

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance of the height of these six students is

  1. A

    22

  2. B

    20

  3. C

    16

  4. D

    18

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    Solution:

    Let x1, x2, x3, x4, x5 be the heights (in cm) of five students of the class. It is given that

          15i=15xi=150   and    18=15i=15xi2(150)2

     i=15xi=750  and   i=15xi2=112590

    Let the mean and variance of the heights of 6 students be X and σ2 respectively. Then,

       X¯=16i=15xi+156=16{750+156}=151

       σ2=16i=15xi2+1562(151)2

     σ2=16112590+15621512=20

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