Background: I am working with real measurements that likely contain two sources of error, (1) measurements that were performed incorrectly, and (2) natural variability of the measured quantity and measurement sensors since different units of the same instrument were used to make the measurements. The real distribution is not necessarily normal, though I expect it to have a single peak, and I can't discard outliers because I can't consistently identify them. (I don't have duplicated values so I would estimate the mode as the peak point of the distribution of measured values.)
I want to find the typical value of the measured quantity. In the past I've had good results using the median, but a colleague asked why I would not use the mode instead. Is the mode more suitable than the median for noisy, possibly skewed data?