When samples are skewed, mean is not a good estimation of central tendency. But instead, median is a better choice.
For cauchy distribution, I heard that there's a completely different estimator (which i didn't understand) that captures the central tendency of it.
And then I came to this new technique called the Highest Density Interval (HDI). It captures the range in which the distribution has the most amount of data points.
Question: If the goal is to measure the central location of a distribution, isn't it simpler to just always report HDI instead of worrying about mean, median, mode, and other more advanced estimators.