Ok ron H your calculations are correct but i believe that the real rms voltage is just the value of the DC voltage because always the rms voltage calculations give a bit greater value that the same calculations for the average voltage value , in this case the rms should be the same as the average what do you think?

also the simulation uses these calculations to calculate the rms

check this 4, 5, 6, 7 the average is (4+5+6+7)/4=5.5
the rms = sqrt((4^2+5^2+6^2+7^2)/4) = 5.56

the result should be the same but there is a small difference because of the squares

What does this mean? Do you think squares and square roots are just approximations? The squares are the reason for the difference. It's not an error. There really is a difference.

OK, try this out:
(10+30+50+70)/4=40
sqrt((10^2+30^2+50^2+70^2)/4)=45.8

Only an 11% error.

 

Vrms (of sine wave) = .707 * Vpeak

Vavg (of rectified sine wave) = 0.637 * Vpeak

About an eleven percent difference, as Ron has noted.

 

Curiosity...

We all know that superposition does not work with power. However, if you run through the integral with a AC signal with a DC bias to obtain an RMS voltage and use this to calculate power, then the result is the same if you linearly added the power delivered by each source.

Eh!