Is there any way of converting the "root mean square" of a set of N measures to the "Standard deviation" of these measures, without knowing the value of N?

If you mean you have the "root mean square" of a set of values then you need to know the mean value to subtract to get the standard deviation.

If you have the "root mean square" of a set of errors (ie the mean value is zero) then the rms **is** the standard deviation.

In neither case do you need 'n'

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