2010-I-11

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

The median

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

The range

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

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

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

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

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