The weight of the new player is 9 kg.
Given -
Mean weight of the team before including the new player = 86.5 kg
Mean weight of the team after including the new player = 86 kg
Number of players in the team before including the new player = 18
To find -
The weight of the new player
Solution -
Let's denote the weight of the new player as 'x' kg.
To solve the problem, we'll use the formula for the mean:
Mean = (Sum of all values) / (Number of values)
- Before including the new player:
The sum of weights of the original 18 players = 86.5 kg * 18
- After including the new player:
The sum of weights of all 19 players = (86 kg * 18) + x kg
According to the problem, the mean weight before including the new player is 86.5 kg, and the mean weight after including the new player is 86 kg. So, we can set up the following equation:
(86.5 kg * 18) = (86 kg * 18) + x kg
Now, let's solve the equation to find the weight of the new player:
(86.5 kg * 18) = (86 kg * 18) + x kg
1557 kg = 1548 kg + x kg
9 kg = x kg
Therefore, the weight of the new player is 9 kg.