Median or mode for measurements with erroneous outliers 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?
 A: It may help to consider two hypothetical scenarios.
Scenario 1) Let the natural variability and sensor error create a fairly symmetric, single modal distribution with a small variance -- like a Normal distribution covering a contextually tight range. At this point the mode=median. Then let the incorrect measurement process randomly take 10% of the measurements and shift them dramatically to the right -- shifting all of them to the right of the median. Now the mode is in the same spot but the median has shifted a little to the right. Under this data generating mechanism, you can make a case for the mode as a "typical" value.
Scenario 2) Let the natural variability and the sensor error create a right skewed distribution with a single mode and a large variance. At this point the mode does not equal the median. Then let the incorrect measurement process randomly take 10% of the measurements and shift them dramatically to the right. Again the mode may be stable and the median may shift to the right, but it is questionable whether either measure represents a "typical" value for this distribution. A single number summary may be too simplistic for this setting.
