The variance of the numbers 2, 3,11 and x is494.find the value x .

The variance of the numbers 2, 3,11 and x is494.find the value x .

  1. A

    6,143

  2. B

    6,145

  3. C

    6,163

  4. D

    None of these

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    Solution:

    From given data, we make the following table

    xx2
    24
    39
    11121
    xx2
    Σx=16+xΣx2=134+x2

    But we know that, variance =Σx2nΣxn2

        134+x2416+x42=494    134+x24256+x2+32x16=494    3x232x+28016=494    280+3x232x=494×16    280+3x232x=196    3x232x+84=0    (x6)(3x14)=0    x=6,x=143

    Therefore, the values of x are 6 and 143.

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