I'm a novice in statistics. I highly appreciate if you could provide me with any piece of information about the following: Is there any statistical test to check whether dispersion measures (standard deviation, mean absolute deviation, or any other) above and below a measure of central tendency (mean, median, mode) are different for one sample. In this question, the concept of skewness is not that helpful to me since, to my limited knowledge, it is not that clear for me to relate a dispersion measure to skewness (correct me if I'm wrong). In fact, given my interest (economics and finance), if the test is available, I may claim that a certain kind of "risk" (e.g., a deviation of any price, rate, or return from the central tendency) is different for one sample above and below the central tendency, when dealing with some empirical analysis.
Thank you very much in advance for your important help.
