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Math Help - variance value

  1. #1
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    variance value

    Hi;

    I know the formula for variance and that a low value means the data is more compact
    and a larger value means spread out more.

    But what does the value actually relate to?
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  2. #2
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    Re: variance value

    Pretty much just what you said: how much the data "varies" or is spread out. Essentially, it tells us how "random" the data is.
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  3. #3
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    Re: variance value

    It is a measure of spread
    for more details look here..:
    Variance - Wikipedia, the free encyclopedia
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  4. #4
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    Re: variance value

    Variance,average distance to the mean squared so lets say I have a data set of

    3,4,6,7 Therfore mean=5

    variance=2.5. I get average distance as 2+1+1+2=6/4 1.5squared equals 2.25.

    Why is this?
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  5. #5
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    Re: variance value

    The average of several numbers which have been squared is not equal to the average of the numbers then squared.

    Suppose you have 2 numbers a and b
    The average of their squares is \frac{a^2+b^2}{2}

    The square of their average is (\frac{a+b}{2})^2=\frac{a^2+2ab+b^2}{4}

    You can see that they are different values.
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