The breakdown performance of the mean and the median continues with their scale estimate counterparts. For a sample X1,..., Xn:
(a) Show that the breakdown value of the sample variance S2 = ∑(Xi) - )2/(n - 1) is 0.
(b) A robust alternative is the median absolute deviation, or MAD, the median of |X1 - M|, |X2 - M|,..., |Xn, - M|, where M is the sample median. Show that this estimator has a breakdown value of 50%.