If you think about it, now averging 256 samples reduces the p-p noise 1/16 or 6.25% of original.
SNR with random noise reduces with time according to the square root of the number of samples average, your observations are "log normal" (pun intended)
However just as in photography, it is always best to capture a better image by technique than try to edit it after with filtering. Averaging is just like a Low Pass filter with 2nd order random noise rejection. Quite often the noise can be random, or recurring from inductive ground leads and switched loads.
Since noise has no DC content ( we call that drift or DC error or Load regulation error) it is best to measure it AC coupled and due to stray inductive effects of the probe near 20MHz, and noise due to no load effects, it is often standard to measure supply noise with 50 ohm cable and 50 ohm scope termination ( Ac coupled). After following this method, use probe leads <=1cm near the output of the regulator or after distribution at the load, consider your scope options.
- pk-pk mode is best for visualizing all noise effects, averaging mode for finding dominant synchnonouse events and remove random noise, but non-avearging mode is usually best with vector dots linked for a continuous trace just to look like the best analog scopes. Memory effects like P-P are just for looking at phantom noise when your DSO cannot display computed RMS, Avg, Vpp to understand where it is coming from.
Triggering to find the synchronous noise events requires skillful use of HF, LF DC, AC and threshold setting as well as choosing external events on other channels. Such as using PWM to trigger a load pulse and then examine the effect on load regulation to determine the ESR and output impedance of the regulator.
But if you understand then the raw non-averaged ( Normal ) signal is best with good probing methods.