2010-I-11

$\begin{array}{cl}
= & \dfrac{18 + 19 +\cdots + 31 + 31}{22} \\
= & 25
\end{array}$

The median

$\begin{array}{cl}
= & \dfrac{26 + 26}{2} \\
= & 26
\end{array}$

The range

$\begin{array}{cl}
= & 31 – 18 \\
= & 13
\end{array}$

1. Let $\mu$ be the mean age of the three new players. Then

   $\begin{array}{rcl}
   \dfrac{18 + 19 + \cdots + 30 + 3 \mu}{23} & = & 25 \\
   488 + 3\mu & = & 575 \\
   3\mu & = & 87 \\
   \mu & = & 29
   \end{array}$

   Therefore, the mean age of the three new players is $29$.

2. $\{25,~31,~31\}$, $\{26,~30,~31\}$.