>one of the strengths of the mean is that it is sensitive to changes in the entire sample, rather than only part of it. Yes but this is exactly what is bad wit

>one of the strengths of the mean is that it is sensitive to changes in the entire sample, rather than only part of it. Yes but this is exactly what is bad with it. At least for the majority of practical applications that I can think of. For instance, if you want to measure the "average" income of the population. If there are a handful of uber-rich people, they will really raise the mean. Even if the vast majority of people make much less than the mean. The median will do a much better job of telling you what a "typical" person makes. I really believe that when most people read or talk about "average", they mentally interpret it as the median. And that the median is generally less misleading. Sure, there are applications where sensitivity to changes at the tails is important. But even then, mean is misleading and difficult to interpret. In your earlier example, if you raised the income of the bottom 10% by 100%, then just use that as a statistic. "The poorest 10% of people now make twice as much money" is much more informative and impressive than "the average income increased by 0.1%."