Low DC power consumption: RMS or mean?
Mean and RMS are two different measurements which both have a use. It's not that mean current is somehow "wrong" and RMS current is "right". The kind of measurement you need will depend on what you plan to do with the value.

RMS is useful for power measurements assuming a constant load resistance, because power is proportional to current squared (or voltage squared), so if you want to e.g. estimate the amount of heat generated by your device, you'll want to use RMS current. On the other hand, if you want to know how long your device can run on a battery of a given capacity in A*h, you'll likely want the average current.

If your supply voltage is constant, you should use the average current for power measurement.