If the standard deviation is a value between 0 and 1, will the variance be less than the standard deviation?

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- Jul 13th 2008, 01:00 PMbillymstandard deviation
If the standard deviation is a value between 0 and 1, will the variance be less than the standard deviation?

- Jul 13th 2008, 01:14 PMBroadhallianReply 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. - Jul 13th 2008, 01:14 PMPlato
Hint: $\displaystyle 0 < x < 1\quad \Rightarrow \quad x^2 < x < \sqrt x $

- Jul 13th 2008, 01:20 PMbillym
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.