Determining the maximum % below average Is there a way to determine the maximum percentage of values that fall below the average in a given sample?  How would someone go about this?  How does this relate to what Markov's inequality and Chebyshev's inequality are saying?

If you take one sample and make it very large, then all the other samples can be below the average. Thus, if you have $n$ samples, it is possible that the number of samples that are below the average is $n-1$. It is impossible to have all $n$ samples below the average, so the quoted maximum value $n-1$ is tight.
