1. Use the data below: (10 Points) Player Salary ($000) Alex Rodriguez 30,000,00
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Question
1. Use the data below: (10 Points) Player Salary ($000) Alex Rodriguez 30,000,000 Andruw Jones 2,000,000 Austin Romine 482,000 Boone Logan 1,875,000 Brad Meyers 480,000 Brett Gardner 2,800,000 CC Sabathia 23,000,000 Cesar Cabral 480,000 Chris Stewart 482,500 Clay Rapada 525,000 Cory Wade 508,925 Curtis Granderson 10,000,000 David Aardsma 500,000 David Robertson 1,600,000 Derek Jeter 15,729,364 Eduardo Nunez 523,800 Eric Chavez 900,000 Freddy Garcia 4,000,000 Hiroki Kuroda 10,000,000 Ivan Nova 527,200 Joba Chamberlain 1,675,000 Mariano Rivera 14,940,025 Mark Teixeira 23,125,000 Michael Pineda 528,475 Nick Swisher 10,250,000 Pedro Feliciano 3,750,000 Phil Hughes 3,200,000 Rafael Soriano 11,000,000 Raul Ibanez 1,100,000 Robinson Cano 14,000,000 Russell Martin 7,500,000 a. Determine the mean, median, and the standard deviation. b. Determine the coefficient of skewness using Pearson’s method. 1. Use the data below: (10 Points) Player Salary ($000) Alex Rodriguez 30,000,000 Andruw Jones 2,000,000 Austin Romine 482,000 Boone Logan 1,875,000 Brad Meyers 480,000 Brett Gardner 2,800,000 CC Sabathia 23,000,000 Cesar Cabral 480,000 Chris Stewart 482,500 Clay Rapada 525,000 Cory Wade 508,925 Curtis Granderson 10,000,000 David Aardsma 500,000 David Robertson 1,600,000 Derek Jeter 15,729,364 Eduardo Nunez 523,800 Eric Chavez 900,000 Freddy Garcia 4,000,000 Hiroki Kuroda 10,000,000 Ivan Nova 527,200 Joba Chamberlain 1,675,000 Mariano Rivera 14,940,025 Mark Teixeira 23,125,000 Michael Pineda 528,475 Nick Swisher 10,250,000 Pedro Feliciano 3,750,000 Phil Hughes 3,200,000 Rafael Soriano 11,000,000 Raul Ibanez 1,100,000 Robinson Cano 14,000,000 Russell Martin 7,500,000 a. Determine the mean, median, and the standard deviation. b. Determine the coefficient of skewness using Pearson’s method.Explanation / Answer
a. The mean, xbar=sigma x/n, where, x is the salary of players, n is the number of players.
=(30000000+...+7500000)/32=212982289/32=6655696.875
For median arrange data in ascending order. For even numbered data (n=32), the median is the average of the two middlemost numbers that is 16th and 17th. Median, Md=(2000000+2800000)/2=2400000.
Standard deviation, sd=sqrt[1/n-1 sigm a(x-xbar)^2]
=sqrt[1/32-1 {(30000000-2400000)^2+...+(7500000-2400000)^2}]=8063029.973
b. Pearson coefficient of skewness=3(Xbar-Md)/sd
=3(6655697-240000)/8063030=2.38
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