Baseball-reference keeps a nice team stat called weighted age, that's basically a team's average age, weighted by playing time. Thus, a young guy who is on the team and never plays won't move the needle much.
So how young are the 2011 Royals?
As young as advertised, as it turns out. Starting with the hitters, we see that the Royals' average age of 26.9 is the youngest in the American League. In fact, this is the youngest group of position players in baseball as well. For a point of reference, the AL average for position players is 29.2, which is also, oddly, the MLB average (the NL is a tenth of a year younger, if you really care). Curiously, the AL Central is a young division. Minnesota has had the next youngest lineups (at 28.0), followed by the Tribe (28.4) and the Tigers (28.5). The Royals have also sent out the youngest pitching staff in the Major Leagues, with an average age of 26.1. Cleveland is second youngest, with an average age of 26.5.
The standard response would be somthing along the lines of "cool, the youth movement truly has begun." And indeed, with the high-profile promotions of Eric Hosmer and Mike Moustakas, along with a number of mid-profile young pitchers, that is the case. In some ways however, the Royals are less young than they are not old, if you catch my drift. Players such as Jeff Francoeur and Melky Cabrera have no long-term future with the Royals (at least on their current contracts) but they are nevertheless relatively young players. Given their stop-gap roles on the team, they could just as easily be 33 or 32, but instead they are both under 27 years old. Conversely, Sean O`Sullivan probably doesn't have much of a future with the team, but he is 23 and the Royals can pretty much keep him under contract for the next half decade, if they wanted to.
In baseball, as in horses and in mathematics, it is better to be young than old. However, there is shockingly little variation amongst baseball teams in this regard. A "young" team has an average age of 26 or 27 an older team might hit 30 in some years (basically depending on how old the Yankees are at any particular moment). It'll be interesting to see how young the Royals averages can get by season's end. The youngest recent group of position players I've found are the 2006 Marlins, who got down to 25.6 in their attempt to field only players making around league minimum. That Marlins team is also the youngest pitching staff of the last five years, with an average age of 25.9.