Question

During the 2011-12 NBA season, LeBron James had an average of 30.3 points per game. The mean and standard deviation for the league were 7.65 points per game and 6.64 points per game, respectively. That same season the WNBA was led by Diana Taurasi who averaged 21.6 points per game. The mean and standard deviation for the entire WNBA that year were 8.13 points per game and 4.77 points per game, respectively. Who had the more remarkable performance compared to the rest of their league

Answer 1

LeBron James had the more remarkable season

Explanation:

Given that:

LeBron James:

Average point per Game = 30.3

Mean of the league (m) = 7.65

Standard deviation (s) = 6.64

WNBA:

Taurasi:

Average point = 21.6

Mean = 8.13

Standard deviation =4.77

Taking the Zscore for each:

LeBron :

Zscore = (x - m) / s

Zscore = (30.3 - 7.65) / 6.64

Zscore = 22.65 / 6.64 = 3.411

P(z < 3.411) = 0.99968

Taurasi :

Zscore = (x - m) / s

Zscore = (21.6 - 8.13) / 4.77

Zscore = 13.47 / 4.77

Zscore = 2.82

P( Z < 2.82) = 0.9976

LeBron's average has more standard deviations above the mean than Taurasi