Consider a sample x1, , xn with n even. Let xL and
Chapter 1, Problem 84(choose chapter or problem)
Consider a sample x1, , xn with n even. Let xL and xUdenote the average of the smallest n/2 and the largest n/2observations, respectively. Show that the mean absolutedeviation from the median for this sample satisfiesouxi 2 ,xuyn = (xU 2 xL)y2Then show that if n is odd and the two averages arecalculated after excluding the median from each half,replacing n on the left with n 2 1 gives the correct result.[Hint: Break the sum into two parts, the first involvingobservations less than or equal to the median and thesecond involving observations greater than or equal tothe median.]
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