In reply to Peter Flom.

For the trimmed and Winsorized means, you have to know in advance how many observations to trim. It becomes circular: to find a robust center, trim the outliers; to trim the outliers, you have to know how many they are; to know how many there are, you need to find a robust center....

From a theoretical point of view, the trimmed/Winsorized means have some nice properties like formulas for standard errors/confidence intervals. However, they are not as robust as the median (which has a high "breakdown value") and, as I said, you have to "tune" them to the data, whereas the median works for all data, regardless of whether you have 5%, 10%, or 20% outliers.

I would consider trimming/Winsorizing if I think that my data are from a contaminated normal distribution. That is, the "real" data are normally distributed, and the outliers are from a symmetric distribution with the same mean. If the data or outliers are skewed (for example, always larger than the population mean), I would not trim/Winsorize.