Samwell Tarly, knowing that a Choosing will be occurring soon, decides to read about the history of past Lord Commanders. He is amazed that Osric was chosen at such a young age.
In the books
In the A Song of Ice and Fire novels, Osric Stark was elected Lord Commander of the Night's Watch at age ten, four hundred years before the War of Conquest, though he ultimately served as Lord Commander for sixty years.
Samwell Tarly specifically brings up the example of Osric Stark to point out that in the centuries-long history of the Night's Watch, boys younger than Jon Snow (who is around 16 years old at that point) have been elected as Lord Commander of the Night's Watch.