How important is castling? How much is it worth? Are there some statistical values for the worth of castling? Are there some numbers, for example in centipawn that can represent the value of castling?
Yes there are some numbers that can (sort of) represent the value of castling.

If you let Stockfish or any other strong engine analyze the starting position, it will generally come to the conclusion that White has roughly a +0.50 advantage. But if you use an opening book (1. Nf3 Nf6 2. Rg1 Ng8 3. Rh1 Nf6 4. Ng1 Ng8 5. Nc3 Nf6 6. Rb1 Ng8 7. Ra1 Nf6 8. Nb1 Ng8) which lets Black castle but not White, the advantage actually flips around, and the starting position advantages Black.

Check these games out:


Stockfish-Xiphos. The starting position, except White can't castle while Black can. Stockfish's starting eval at depth 31/48 is -0.20. (Yes Stockfish wins anyway, but it is Stockfish, the strongest conventional engine in the world, playing)
Xiphos-Stockfish. The reverse game. Xiphos plays 1. Nc3 evaluating the position as 0.00, while Stockfish is -0.84 at depth 36/52.
AllieStein-Stockfish. Played from the opening position with both sides able to castle. AllieStein gave 0.43 advantage to White at depth 18/57.
Stockfish-Alliestein. The reverse game, Stockfish gave White a 0.47 advantage in the opening position at depth 38/59.