52. Let X1, . . . , Xn be a random sample from a pdf that is symmetric about m. An estimator for m that has been found to perform well for a variety of underlying distributions is the Hodges–Lehmann estimator.

To de ne it, rst compute for each i j and each j

1, 2, . . . , n the pairwise average  (Xi  Xj)/2.

Then the estimator is  the median of the s.

Compute the value of this estimate using the data of Exercise 41 of Chapter 1. (Hint: Construct a square table with the xi s listed on the left margin and on top.

Then compute averages on and above the diagonal.)