Experimentally measuring the gain of an amplifier with noise
The term "mean value of a perfect DC voltage' is redundant. A perfect DC voltage is always the same, so the mean, mode, and median averages are all identical to the instantaneous voltage at any time. However in practice a 'perfect' DC voltage is impossible, because at some time the voltage had to change to become what it is. Therefore any measurement will always be an average over some time period.   

You can average out high frequency noise to get a more accurate 'DC' reading. However if you take the mean average the result will be lower than the rms value. If you have a 1V DC signal with 1V peak sine wave 'noise' voltage on it (so the peaks are 0V and 2V) the mean average will still be 1V but the rms voltage will be 1.2152V.