Final answer:
The mean weight of the five rugby players, after the new player joins, is calculated to be 82 kg by adding the new player's weight to the total and dividing by the number of players.
Step-by-step explanation:
The mean weight of the four rugby players is 80 kg. We can calculate the total weight of the four players by multiplying the mean weight by the number of players, getting 4 × 80 kg = 320 kg.
When a fifth player weighing 90 kg joins, the new total weight is 320 kg + 90 kg = 410 kg. To find the new mean weight of the five players, we divide the total weight by the number of players: 410 kg / 5 = 82 kg.
Therefore, the mean weight of the five rugby players is 82 kg.