# Uncertainty on standard deviation and rms

Say I have a time-series of a parameter $y(t)$. Each value of $y(t)$ has an uncertainty of $\epsilon_y$ due to how it was measured. What is the uncertainty on the calculated rms or standard deviation?

As an example, say I was measuring a voltage signal $V(t)$. The voltage measurement device has a specified uncertainty ($\epsilon_V$) of 0.5%. If I want to say the AC voltage signal had an RMS of 240 volts $\pm \epsilon_{RMS}$, how would I know the uncertainty on the rms?

• By uncertainty do you mean standard deviation or is Ey a noise term or is this a reference to something else? Is this series independent or (as is more typical for time series), related over time? Aug 3, 2016 at 4:13
• Ey is an uncertainty on my term. For example, say I was measuring an AC voltage signal, I would have an uncertainty on my voltage measurement (Ev). If I work out the RMS of the voltage, it will have some uncertainty (presumably based on Ev)? Aug 3, 2016 at 4:14
• what does the uncertainty actually quantify in your case? Aug 3, 2016 at 4:22
• My voltage measurement (in this example only) is 95% confident of its measurement being within 0.5%. Aug 3, 2016 at 4:43
• Sorry - can you clarify what the word "95% confident" means in this context?... is it assuming some distribution around a true mean - like uniform or normal errors or some such? Is "95% confident" really implying an actual confidence interval, or is this really saying something else? [And you may not know answers to all these, but on the other hand may be in a position to suggest pointers to the information]. It's not clear what the underlying 'model' of the uncertainty is here Aug 3, 2016 at 6:20