State whether it is the mean or median that minimizes the mean absolute deviation

State whether it is the mean or median that is the balance point on a balance scale

In the section "What is central tendency,
we saw that the center of a distribution could be defined three
ways: (1) the point on which a distribution would balance, (2)
the value whose average absolute
deviation from all the other values is minimized, and (3)
the value whose squared difference from all the other values is
minimized. From the simulation in this chapter, you discovered
(we hope) that the mean is the point on which a distribution would
balance, the median is the value that minimizes the sum of absolute
deviations, and the mean is the value that minimizes the sum of
the squared values.

When a distribution is symmetric, then the mean,
and the median are the same.