Therein lies a tail… Even in the first, thermometer, problem, there is still a question about whether to average or to take the median. Roughly speaking, if one expects some form of independent random additive noise in each thermometer, the choice of what to do with outliers depends on what one’s prior for the expected noise distribution looks like. If one expects a gaussian, the variance of the distribution is finite, and one does better by averaging the readings. If one expects a distribution with long tails, with an unbounded variance, then one wants to pick the estimate more nearly from the median. Intermediate choices include throwing out some outliers and averaging the remaining samples or ranking the samples, then doing a weighted average of the samples based on how far from the median rank they are. A nice example for the Cauchy distribution is at http://kmh-lanl.hansonhub.com/publications/maxent93.pdf
Therein lies a tail… Even in the first, thermometer, problem, there is still a question about whether to average or to take the median. Roughly speaking, if one expects some form of independent random additive noise in each thermometer, the choice of what to do with outliers depends on what one’s prior for the expected noise distribution looks like. If one expects a gaussian, the variance of the distribution is finite, and one does better by averaging the readings. If one expects a distribution with long tails, with an unbounded variance, then one wants to pick the estimate more nearly from the median. Intermediate choices include throwing out some outliers and averaging the remaining samples or ranking the samples, then doing a weighted average of the samples based on how far from the median rank they are. A nice example for the Cauchy distribution is at http://kmh-lanl.hansonhub.com/publications/maxent93.pdf