If each observation of a raw data whose variance is σ2 ismultiplied by h, then the variance of the new set is

If each observation of a raw data whose variance is σ2 is

multiplied by h, then the variance of the new set is

  1. A

    σ2

  2. B

    h2σ2

  3. C

    h σ2

  4. D

    h+ σ2

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    Solution:

    Let x1,x2,,xn be a raw data. Then,

    σ2=1ni=1nxiX¯2

    If each value is multiplied by h, then the values are

    hx1,hx2,,hxn.The AM of the new values is

    hx1+hx2++hxnn=hX¯.

    The variance σ2 of the new set of values is given by

    σ12=1ni=1nhxihX¯2=h21ni=1nxiX¯2=h2σ2.

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