In data analysis, when are the use of these different means appropriate?
For example, I'm using data to infer the peak of waveforms at different points around a semicircle. If my data has intensity $8.0$ (local maximum) at $\theta = -55.554, -55.693, -55.868, -56.063$, what is the appropriate average/mean function to use to infer the actual peak of the waveform?