  It is well known that the time average or the center of mass for generic
orbits of the standard tent map is 0.5. In this paper we show some interesting
properties of the exceptional orbits, including periodic orbits, orbits without
mass center, and orbits with mass centers different from 0.5. We prove that for
any positive integer $n$, there exist $n$ distinct periodic orbits for the
standard tent map with the same center of mass, and the set of mass centers of
periodic orbits is a dense subset of $[0,2/3]$. Considering all possible
orbits, then the set of mass centers is the interval $[0,2/3]$. Moreover, for
every $x$ in $[0,2/3]$, there are uncountably many orbits with mass center $x$.
We also show that there are uncountably many orbits without mass center.
