Middle School

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If the mean weight of 4 backfield members on a football team is 222 lb and the mean weight of the 7 other players is 198 lb, what is the mean weight of the 11-person team?

Answer :

Final answer:

The mean weight of the 11-person team is approximately 206.73 pounds. The California quarterback's weight is closer to his team's mean than the Texas player's weight is to his team's mean, indicating the quarterback is comparatively lighter with respect to his own team.

Explanation:

To find the mean weight of the 11-person team, we calculate the total weight of all team members and then divide by the number of team members. The total weight of the backfield members is 4 members × 222 lb/member = 888 lb. The total weight of the other players is 7 members × 198 lb/member = 1386 lb. The total weight of the 11-person team is 888 lb + 1386 lb = 2274 lb.

The mean weight for the 11-person team is 2274 lb ÷ 11 members = 206.727... lb, which rounds to approximately 206.73 lb. This is the mean weight for the 11-person team.

Regarding the quarterback who once weighed 205 pounds, we need to calculate his weight in terms of standard deviations from the team mean. The formula for z-score is (individual value - mean) ÷ standard deviation. However, this problem doesn't provide the standard deviation for the 11-person team, so we cannot calculate the z-score for the famous quarterback without further information. Nonetheless, we can compare him to the player from the Texas football team, whose mean weight is 240.08 pounds and whose standard deviation is 44.38 pounds.

The Texas player's weight is 209 pounds. His z-score is calculated as follows: (209 lb - 240.08 lb) ÷ 44.38 lb = -0.70. This indicates that the Texas player is 0.70 standard deviations below the mean of his team.

Since the famous quarterback's weight of 205 pounds is closer to the mean of his team (206.73 pounds) than the Texas player's weight is to his team's mean (240.08 pounds), we can deduce that the quarterback is comparatively lighter with respect to his own team.

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Rewritten by : Barada

To find the Mean or Average you have to add up all numbers it is asking for which in case are 222 and 198.

so you will add 222+198

That will equal 420

Then you will divide with the amount added together which is 2

420/2=210

so the mean of the 11 people is 210 or 210lbs