Answer :
The mean weight of the 9-person team is 220 lb.
To find the mean weight of the 9-person team, we need to calculate the total weight of all the players and divide it by the total number of players.
Let's denote the mean weight of the outfielders as "M1" and the mean weight of the other players as "M2".
Given:
Mean weight of 3 outfielders = 190 lb
Mean weight of 6 other players = 235 lb
We know that the mean weight is calculated by dividing the total weight by the number of players. Therefore, we can set up the following equations:
M1 = Total weight of outfielders / Number of outfielders
M2 = Total weight of other players / Number of other players
To find the total weight of the outfielders, we multiply the mean weight by the number of outfielders:
Total weight of outfielders = M1 * Number of outfielders
Similarly, to find the total weight of the other players, we multiply the mean weight by the number of other players:
Total weight of other players = M2 * Number of other players
Since we want to find the mean weight of the entire 9-person team, we need to consider all players. Therefore, the total weight of all players is the sum of the total weight of outfielders and the total weight of other players:
Total weight of all players = Total weight of outfielders + Total weight of other players
Now, let's substitute the known values into the equations:
M1 = 190 lb
Number of outfielders = 3
M2 = 235 lb
Number of other players = 6
Total weight of outfielders = M1 * Number of outfielders = 190 lb * 3 = 570 lb
Total weight of other players = M2 * Number of other players = 235 lb * 6 = 1410 lb
Total weight of all players = Total weight of outfielders + Total weight of other players = 570 lb + 1410 lb = 1980 lb
Finally, to find the mean weight of the 9-person team, we divide the total weight of all players by the total number of players:
Mean weight of the 9-person team = Total weight of all players / Total number of players
= 1980 lb / 9
= 220 lb
Therefore, the mean weight of the 9-person team is 220 lb.
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