Statistical noise measurement
If you have the average value of the data set you are interested in and all you want to compute is standard deviation (or RMS because it is the same) then: -


Subtract a sample value from the average
Square that new value
Sum all the squared values
Divide the total by the number of samples
Take the square root


If the noise is small and might contain quantization noise then you are going to be less accurate with the noise value computed.

If the mean/average is expected to drift in time then you may choose to use a rolling average calculation so that a significant emerging offset does not make the noise value bigger than it actually is.