  In this article the extremal structures for the mean order of connected
induced subgraphs of cographs are determined. It is shown that among all
connected cographs of order $n \ge 7$, the star $K_{1,n-1}$ has maximum mean
connected induced subgraph order, and for $n \ge 3$, the $n$-skillet, $K_1+(K_1
\cup K_{n-2})$, has minimum mean connected induced subgraph order. It is
deduced that the density for connected cographs (i.e. the ratio of the mean to
the order of the graph) is asymptotically $1/2$. The mean order of all
connected induced subgraphs containing a given vertex $v$ of a cograph $G$,
called the local mean of $G$ at $v$, is shown to be at least as large as the
mean order of all connected induced subgraphs of $G$, called the global mean of
$G$.
