Currently, professional men’s basketball players score an average of 18.2 points per game with a standard deviation of 4.5 points. The current top-scoring professional basketball player scores an average of 36.2 points per game. In one season in the 1990s, professional basketball players averaged 13.2 points per game with a standard deviation of 3.7 points. The top-scoring professional basketball player averaged 30.1 points per game. Which player did better relative to his peers?
Answer
A
The 1990s basketball player did better than the current basketball player because his z-score is higher.
B
The current basketball player did better than the 1990s basketball player because his z-score is higher.
C
The 1990s basketball player did better than the current basketball player because his z-score is closer to the mean.
D
The current basketball player did better than the 1990s basketball player because his z-score is closer to the mean.
Explanation
Compare each player’s score to his peers using a z-score: subtract the season average and divide by the standard deviation. The current player’s z-score is (36.2 − 18.2) ÷ 4.5 = 4.0, while the 1990s player’s is (30.1 − 13.2) ÷ 3.7 ≈ 4.57. Since 4.57 is higher than 4.0, the 1990s player scored farther above his peers’ average and did better relative to them.
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