Consider the discussion in our Devore reading in this unit involvingan important distinction between mean and median that uses the concept of a trimmed mean tohighlight an important continuum between the two. Presuming that the mean and median are different valuesfor a distribution, the meancan betaken to indicate a 0% trim, and the mediancan be taken to approach a 50% trim (with effectively 100% of the values removed). These two values define a continuum of trimmed mean values that would fall between the two.

Discuss why the mean and median of the distribution always approach each other as we take trimmed means at higher and higher percentages (e.g., 10%, 20%, 30% ...). In particular, describe what is happening to the kurtosis and skewness of the distribution as we trim off more and more data. Speculate on whether or not you might expect to see an optimum point in that process at some value between the mean and median. Why might this matter?