I just experimented again today on using a GW-INSTEK GFG-8019G function generator to produce ~50Hz square and sine wave. I measure the waveforms using a HP 54600B 100MHz oscilloscope to know roughly the expected measurement values and measure them using 4 different multimeters: Victor VC921, Radio-shack 22-812, Fluke 17B and Appa 207. Except for the Appa 207 which is true RMS, the rest just uses (I presume) averaging method when measuring AC.
I know that's a lot of equipments for a normal electronics hobbyist, but I can't resist buying cheap test gears from eBay from time to time
Below is the result:
Sine wave which measures 3.844V peak-to-peak and 1.357V RMS on oscilloscope reads 1.329, 1.340 and 1.346V on the averaging meters and 1.3527V on the true rms multimeter.
Square wave which measures 3.906V peak-to-peak and 1.922V RMS on oscilloscope reads 2.108V, 2.129V and 2.141V on the averaging meters and and 1.939V on the true rms multimeter.
So with a sine wave, all meters show approximately the correct value. With a square wave, the averaging meters show higher than the expected rms value, and only the Appa 207 (true RMS) shows the correct value. So the Appa 207 is indeed true RMS.
One thing I notice is that the AC voltage measurement in the averaging meters is good to about 1kHz only - any frequency higher than that will read lower value. The Appa 207 multimeter can still measure the RMS value of frequency in the range of 50kHz. Did not try higher frequency though.
Attached are some of the photos taken during the experiment.