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Math Help - standard deviation

  1. #1
    Member billym's Avatar
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    standard deviation

    If the standard deviation is a value between 0 and 1, will the variance be less than the standard deviation?
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  2. #2
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    Reply to the question

    Yes as far as I can tell.

    If it was to be between 0 and 1 then it would be in decimal form.

    Using the fact that the Standard Deviation^2 = Variance.

    multiplying a decimal number by itself will end up making it less than its original value.

    Not really conclusive proof at all.
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  3. #3
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    Hint: 0 < x < 1\quad  \Rightarrow \quad x^2  < x < \sqrt x
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  4. #4
    Member billym's Avatar
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    I figured as much since the variance is the square of the SD... its just strange to picture the SD being greater than the variance.
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