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cooper2017
cooper2017
03.03.2021 • 
Mathematics

Instructions Use the table and the data provided to analyze the 2015/2016 points per game for the LA Lakers.

Players Average points per game 2015/2016
x Deviation from the Mean
(x−µ) Square of the Deviation
(x−µ)² z-Score
x−µ
σ
Anthony Brown 4.0
Brandon Bass 7.2
D'Angelo Russell 13.2
Jordan Clarkson 15.5
Julius Randle 11.3
Kobe Bryant 17.6
Larry Nance Jr. 5.5
Louis Williams 15.3
Marcelo Huertas 4.5
Metta World Peace 5.0
Nick Young 7.3
Robert Sacre 3.5
Roy Hibbert 5.9
Ryan Kelly 4.2
Tarik Black 3.4
Total Σx = Σ(x − µ)² =
Source: http://www.espn.com/nba/team/stats/_/name/lal/los-angeles-lakers
Part A: Complete the table. (5 points)

Calculate the mean (µ) for the players listed.
Fill in the table by calculating the deviation from the mean, (x − µ), the square of the deviation, (x − µ)², and the sum of the squares of the deviation.
Calculate the variance.
Calculate the standard deviation.
Calculate the z-score for each player.
Part B: Answer the following questions. (15 points)

What does the z-score determine?
Analyze the player's average points per game that is farthest from the mean. Evaluate the z-score and justify whether it is reasonable.
Analyze the player's average points per game that is closest to the mean. Evaluate the z-score and justify whether it is reasonable.
Explain why negative z-scores are present.
What is the sum of the z-scores? Evaluate your calculation and justify it with statistical reasoning.
Part C: Compare the data. (10 points)

Use the table presented below for z-scores for the salaries of the LA Lakers in 2015/2016.

Player Salary 2015/2016
x z-Score
x−µ
σ
Anthony Brown $525,093 −0.65
Brandon Bass $3,000,000 −0.27
D'Angelo Russell $5,103,120 0.05
Jordan Clarkson $845,059 −0.60
Julius Randle $3,132,240 −0.25
Kobe Bryant $25,000,000 3.07
Larry Nance Jr. $1,155,600 −0.55
Lou Williams $7,000,000 0.33
Marcelo Huertas $525,093 −0.65
Metta World Peace $1,499,187 −0.50
Nick Young $5,219,169 0.06
Robert Sacre $981,358 −0.58
Roy Hibbert $15,514,031 1.63
Ryan Kelly $1,724,250 −0.47
Tarik Black $845,059 −0.60

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