Suppose we are looking at a right-skewed size distribution such as the distributions of income, casualty losses, or flood sizes, and we want to look at some alternative measures to jointly represent the central tendency of that distribution. The median -- the ratio of, e.g., income per person where half the people have incomes above that ratio and half below -- is one appealing measure. Is there any commonly used, named statistic that represents the level of income where half of the dollars of income (loss value, gallons of water) are received by people (accidents, floods) above that level and half below?
If so, does it have a name? A literature? In right-skewed populations, will these two statistics bracket the mean?
