Question

a basketball team played six games. in those games, the team won by 8 points, lost by 4, won by 7, won by 10, lost by 3, and won by 12. what was the mean difference in game scores over the six games? the mean difference in game scores over the six games was \boxed{}.

Explanation:

Step1: Define wins and losses

Let wins be positive and losses be negative. The differences are: \(+8\), \(-4\), \(+7\), \(+10\), \(-3\), \(+12\).

Step2: Sum the differences

Sum \(= 8 - 4 + 7 + 10 - 3 + 12\)
\(= (8 + 7 + 10 + 12) + (-4 - 3)\)
\(= 37 - 7\)
\(= 30\).

Step3: Calculate the mean

Mean \(= \frac{\text{Sum}}{\text{Number of games}} = \frac{30}{6}\)
\(= 5\).

Answer:

5