. (The Excel file BASE.XLS, found on the CD that came with your Berk and Carey t

Question

. (The Excel file BASE.XLS, found on the CD that came with your Berk and Carey text, has average career batting averages for 263 major league baseball players at the start of the 1988 season. a. Calculate descriptive data statistics (e.g., mean, median, and standard deviation) for the batting averages. b. Obtain a histogram for the batting averages of the players and print out with appropriate title, legend and axis scaling. Interpret your results. c. Divide the data into three sub-populations: rookies (those players with only 1 year of experience); young players (those players with less than 6 years of experience); and veterans (those players with 6 or more years of experience). Use the STATS add-in provided by the Berk and Carey text to create a single graph which contains four boxplots corresponding to the batting averages of: 1) all 263 players; 2) rookies; 3) young players, and, 4) veterans. Please make sure the graph is properly labeled and that the y-scale is modified to go from 0.180 to 0.360. d. Interpret fully the results found in part c paying particular attention to the presence of outliers, the difference in variation, the relative values of percentiles and any other contrasts that you might find interesting between the batting averages in these populations of baseball players.

First Last League Division Team Position Years Aver Career Salary Barry Bonds N E Pit. CF 1 0.223 100 Bobby Bonilla N W Pit. O1 1 0.256 115 Cory Snyder A E Cle. OS 1 0.272 90 Dale Sveum A E Mil. 3B 1 0.246 70 Glenn Braggs A E Mil. LF 1 0.237 70 John Kruk N W S.D. LF 1 0.309 110 Kal Daniels N W Cin. OF 1 0.320 87 Kurt Stillwell N W Cin. SS 1 0.229 75 Mike Aldrete N W S.F. 1O 1 0.250 75 Mike Kingery A W Sea. OF 1 0.258 68 Pete Incaviglia A W Tex. RF 1 0.250 172 Rey Quinones A E Sea. SS 1 0.218 70 Ruben Sierra A W Tex. OF 1 0.264 98 Robby Thompson N W S.F. 2B 1 0.271 140 Will Clark N W S.F. 1B 1 0.287 120 Wally Joyner A W Cal. 1B 1 0.290 165 Andres Galarraga N E Mon. 1B 2 0.255 92 Al Newman A E Min. 2B 2 0.196 70 Andres Thomas N W Atl. SS 2 0.252 75 Bob Melvin N W S.F. C 2 0.223 90 Billy Jo Robidoux A E Mil. 1B 2 0.216 68 Curt Ford N E St.L. OF 2 0.261 70 Dan Pasqua A E N.Y. LF 2 0.264 110 John Cangelosi N W Pit. LF 2 0.234 100 Jose Canseco A W Oak. LF 2 0.249 165 Jack Howell A W Cal. 3B 2 0.236 95 Kevin Mitchell N E S.D. OS 2 0.275 125 Len Dykstra N E N.Y. CF 2 0.280 203 Mike Diaz N E Pit. O1 2 0.269 90 Mariano Duncan N W L.A. SS 2 0.237 150 Ozzie Guillen A W Chi. SS 2 0.261 175 Oddibe McDowell A W Tex. CF 2 0.255 200 Steve Buechele A W Tex. 3B 2 0.235 135 Shawon Dunston N E Chi. SS 2 0.253 155 Steve Lombardozzi A W Min. 2B 2 0.243 105 Vince Coleman N E St.L. LF 2 0.250 160 Alvin Davis A W Sea. 1B 3 0.281 480 Argenis Salazar A W K.C. SS 3 0.212 100 Billy Hatcher N W Hou. CF 3 0.252 110 Chris Brown N W S.F. 3B 3 0.293 215 Daryl Boston A W Chi. CF 3 0.233 75 Danny Tartabull A W K.C. RF 3 0.277 145 Eric Davis N W Cin. LF 3 0.259 300 Glenn Davis N W Hou. 1B 3 0.264 215 Herm Winningham N E Mon. OF 3 0.239 90 Jim Presley A W Sea. 3B 3 0.262 200 Jeff Reed N W Mon. C 3 0.224 75 John Russell N E Phi. C 3 0.240 155 Jose Uribe N W S.F. SS 3 0.230 195 Kirby Puckett A W Min. CF 3 0.304 365 Larry Sheets A E Bal. DH 3 0.271 145 Mike LaValliere N E Pit. C 3 0.221 100 Mike Pagliarulo A E N.Y. 3B 3 0.239 175 Mark Salas A W Min. C 3 0.266 137 Mickey Tettleton A W Oak. C 3 0.233 120 Milt Thompson N E Phi. CF 3 0.276 140 Rob Deer A E Mil. RF 3 0.218 215 Rick Schu N E Phi. 3B 3 0.260 140 Scott Bradley A W Sea. C 3 0.276 90 Terry Pendleton N E St.L. 3B 3 0.255 160 Andy Van Slyke N E Pit. RF 4 0.259 550 Bill Schroeder A E Mil. UT 4 0.231 180 Carmelo Martinez N W S.D. O1 4 0.249 340 Curt Wilkerson A W Tex. 2S 4 0.242 230 Dave Anderson N W L.A. 3S 4 0.227 225 Darnell Coles A E Det. 3B 4 0.252 105 Dan Gladden A W Min. CF 4 0.281 210 Donnie Hill A W Chi. 23 4 0.273 275 Dick Schofield A W Cal. SS 4 0.221 475 Darryl Strawberry N E N.Y. RF 4 0.260 1220 Greg Gagne A W Min. SS 4 0.236 155 Harold Reynolds A W Sea. 2B 4 0.209 88 Joe Carter A E Cle. RF 4 0.279 250 Juan Samuel N E Phi. 2B 4 0.268 640 Joel Skinner A W N.Y. C 4 0.240 110 Kevin McReynolds N W N.Y. CF 4 0.263 625 Mitch Webster N E Mon. CF 4 0.282 210 Marvell Wynne N W S.D. OF 4 0.248 240 Phil Bradley A W Sea. LF 4 0.302 750 Ronn Reynolds N E Pit. LF 4 0.205 190 Rafael Santana N E N.Y. SS 4 0.245 250 Sid Bream N E Pit. 1B 4 0.253 200 Steve Jeltz N E Phi. SS 4 0.208 150 Spike Owen A W Bos. SS 4 0.235 350 Tony Fernandez A E Tor. SS 4 0.295 350 Tom Foley N E Mon. UT 4 0.248 250 Tim Hulett A W Chi. 3B 4 0.245 185 Tim Teufel N E N.Y. 2B 4 0.261 278 Buddy Biancalana A W K.C. SS 5 0.213 175 Bill Doran N W Hou. 2B 5 0.274 625 Brook Jacoby A E Cle. 3B 5 0.275 613 Carmen Castillo A E Cle. OD 5 0.254 248 Don Mattingly A E N.Y. 1B 5 0.332 1975 Don Slaught A W Tex. C 5 0.278 432 George Bell A E Tor. LF 5 0.287 1175 Greg Brock A W Mil. 1B 5 0.233 385 Gary Pettis A W Cal. CF 5 0.251 400 Gary Redus A E Chi. LF 5 0.248 400 Greg Walker A W Chi. 1B 5 0.275 500 Glenn Wilson N E Phi. RF 5 0.270 663 Howard Johnson N E N.Y. 3S 5 0.252 298 Julio Franco A E Cle. SS 5 0.288 775 John Moses A W Sea. CF 5 0.249 80 Kevin Bass N W Hou. RF 5 0.274 630 Marty Barrett A E Bos. 2B 5 0.281 575 Mike Young A E Bal. LF 5 0.257 350 Pat Sheridan A E Det. OF 5 0.262 190 Rafael Belliard N E Pit. SS 5 0.232 130 Randy Bush A W Min. LF 5 0.247 300 Ron Kittle A W N.Y. DH 5 0.231 425 Tony Gwynn N W S.D. RF 5 0.326 740 Tony Phillips A W Oak. 2B 5 0.257 425 Wade Boggs A E Bos. 3B 5 0.352 1600 Willie McGee N E St.L. CF 5 0.298 700 Alan Wiggins A E Bal. 2B 6 0.263 700 Bob Brenly N W S.F. C 6 0.254 600 Brett Butler A E Cle. CF 6 0.277 765 Chris Bando A E Cle. C 6 0.236 305 Chili Davis N W S.F. RF 6 0.270 815 Candy Maldonado N W S.F. OF 6 0.243 415 Cal Ripken A E Bal. SS 6 0.289 1350 Dave Henderson A W Bos. OF 6 0.255 325 Gary Gaetti A W Min. 3B 6 0.254 900 Jesse Barfield A E Tor. RF 6 0.273 1238 Jody Davis N E Chi. C 6 0.254 1008 Johnny Ray N E Pit. 2B 6 0.288 657 John Shelby A E Bal. OF 6 0.240 300 Kent Hrbek A W Min. 1B 6 0.289 1310 Len Matuszek N W L.A. O1 6 0.237 265 Mel Hall A E Cle. LF 6 0.281 550 Mike Marshall N W L.A. RF 6 0.268 670 Pat Tabler A E Cle. 1B 6 0.288 580 Rick Leach A E Tor. DO 6 0.257 250 Ron Roenicke N E Phi. OF 6 0.248 191 Ryne Sandberg N E Chi. 2B 6 0.287 740 Steve Balboni A W K.C. 1B 6 0.235 100 Scott Fletcher A W Tex. SS 6 0.263 475 Steve Sax N W L.A. 2B 6 0.284 740 Tom Brunansky A W Min. RF 6 0.248 940 Tim Laudner A W Min. C 6 0.225 245 Von Hayes N E Phi. 1B 6 0.276 1300 Wayne Tolleson A W N.Y. 3B 6 0.255 385 Bob Dernier N E Chi. CF 7 0.254 708 Bob Kearney A W Sea. C 7 0.235 300 Eddie Milner N W S.F. CF 7 0.255 490 Harold Baines A W Chi. RF 7 0.287 950 Hubie Brooks N E Mon. SS 7 0.278 750 Ken Phelps A W Sea. DH 7 0.235 300 Leon Durham N E Chi. 1B 7 0.281 1183 Lloyd Moseby A E Tor. CF 7 0.261 788 Mike Davis A W Oak. RF 7 0.268 780 Mike Scioscia N W L.A. C 7 0.264 875 Mookie Wilson N E N.Y. OF 7 0.277 800 Ozzie Virgil N W Atl. C 7 0.240 700 Rafael Ramirez N W Atl. S3 7 0.263 875 Terry Harper A W Det. OF 7 0.254 425 Tito Landrum N E St.L. OF 7 0.256 287 Tony Pena N E St.L. C 7 0.286 1150 Tim Wallach N E Mon. 3B 7 0.254 750 Vance Law N E Mon. 2B 7 0.250 525 Wally Backman N E N.Y. 2B 7 0.285 550 Bruce Bochy N W S.D. C 8 0.248 135 Ed Romero A E Bos. SS 8 0.249 375 Garth Iorg A E Tor. 32 8 0.265 363 Gary Ward A W N.Y. LF 8 0.289 600 Kirk Gibson A E Det. RF 8 0.275 1300 Rickey Henderson A E N.Y. CF 8 0.290 1670 Tony Bernazard A E Cle. 2B 8 0.264 530 Tom Brookens A E Det. UT 8 0.247 342 Tim Flannery N W S.D. 2B 8 0.260 327 Tommy Herr N E St.L. 2B 8 0.276 925 Willie Upshaw A E Tor. 1B 8 0.268 960 Alex Trevino N W L.A. C 9 0.249 513 Carney Lansford A W Oak. 3B 9 0.292 1200 Damaso Garcia N E Cin. 2B 9 0.286 850 Dwayne Murphy A W Oak. CF 9 0.248 600 Glenn Hubbard N W Atl. 2B 9 0.242 535 Harry Spilman N W S.F. 1B 9 0.236 175 Keith Moreland N E Chi. RF 9 0.286 1043 Mike Heath A E Det. C 9 0.248 650 Ozzie Smith N E St.L. SS 9 0.247 1940 Paul Molitor A E Mil. 3B 9 0.291 1260 Ron Hassey A E Chi. C 9 0.282 560 Ron Oester N W Cin. 2B 9 0.266 750 Terry Kennedy A W Bal. C 9 0.272 920 Alan Trammell A E Det. SS 10 0.281 517 Bo Diaz N W Cin. C 10 0.259 750 Eddie Murray A E Bal. 1B 10 0.299 2460 Jeffrey Leonard N W S.F. LF 10 0.273 900 Jim Morrison N E Pit. 3B 10 0.266 278 Ken Landreaux N W L.A. OF 10 0.271 738 Ken Oberkfell N W Atl. 3B 10 0.283 725 Lance Parrish N E Phi. C 10 0.263 800 Lou Whitaker A E Det. 2B 10 0.281 420 Rance Mulliniks A E Tor. 3B 10 0.268 450 Rob Wilfong A W Cal. 2B 10 0.249 342 Terry Puhl N W Hou. OF 10 0.281 900 Andre Dawson N E Chi. RF 11 0.280 500 Alfredo Griffin A W Oak. SS 11 0.257 750 Dale Murphy N W Atl. CF 11 0.277 1900 Garry Templeton N W S.D. SS 11 0.284 738 Jim Gantner A E Mil. 2B 11 0.275 850 Joel Youngblood N W S.F. OF 11 0.268 450 Ray Knight A E Bal. 3B 11 0.278 500 Willie Wilson A W K.C. CF 11 0.297 1000 Chet Lemon A E Det. CF 12 0.277 675 Craig Reynolds N W Hou. SS 12 0.259 417 Denny Walling N W Hou. 3B 12 0.278 595 Jack Clark N E St.L. 1B 12 0.275 1300 Larry Herndon A E Det. OF 12 0.273 225 Rick Burleson A W Bal. UT 12 0.275 450 Rick Cerone A E N.Y. C 12 0.238 250 Rick Manning A E Mil. OF 12 0.258 400 Roy Smalley A W Min. DH 12 0.256 740 Willie Randolph A E N.Y. 2B 12 0.274 875 Andre Thornton A E Cle. DH 13 0.256 1100 Bill Almon N E Pit. UT 13 0.255 240 Gary Carter N E N.Y. C 13 0.271 1926 Jerry Mumphrey N E Chi. OF 13 0.288 600 Jim Rice A E Bos. LF 13 0.303 2413 Jim Sundberg N W Chi. C 13 0.250 825 Keith Hernandez N E N.Y. 1B 13 0.302 1800 Larry Parrish A W Tex. DH 13 0.266 588 Mike Easler N E Phi. DH 13 0.294 700 Robin Yount A E Mil. CF 13 0.287 1000 Alan Ashby N W Hou. C 14 0.242 475 Brian Downing A W Cal. LF 14 0.266 900 Bill Madlock N W L.A. 3B 14 0.307 850 Doug DeCinces A W Cal. 3B 14 0.261 850 Dave Parker N W Cin. RF 14 0.301 1042 Dave Winfield A E N.Y. RF 14 0.286 1861 Frank White A W K.C. 2B 14 0.260 750 George Brett A W K.C. 3B 14 0.314 1500 Jim Dwyer A E Bal. DO 14 0.255 275 Jerry Royster A W Chi. UT 14 0.250 250 Ken Griffey N E Atl. OF 14 0.300 1000 Phil Garner N W Hou. 3B 14 0.262 450 Buddy Bell N W Cin. 3B 15 0.282 775 Dwight Evans A E Bos. RF 15 0.268 933 Davey Lopes N E Hou. 3O 15 0.263 450 Gary Matthews N E Chi. LF 15 0.282 733 Juan Beniquez A E K.C. UT 15 0.275 430 Johnny Grubb A E Det. DH 15 0.280 365 Lee Lacy A E Bal. RF 15 0.289 525 Mike Schmidt N E Phi. 3B 15 0.268 2127 Chris Speier N E S.F. 3S 16 0.246 275 Darrell Porter A W Tex. CD 16 0.247 260 George Hendrick A W Cal. OF 16 0.279 700 Ron Cey A E Oak. 3B 16 0.261 1050 Carlton Fisk A W Chi. C 17 0.271 875 Don Baylor A E Bos. DH 17 0.263 950 Dave Concepcion N W Pit. UT 17 0.267 320 Jose Cruz N W Hou. LF 17 0.287 773 Tom Paciorek A W Tex. UT 17 0.282 235 Bill Buckner A E Bos. 1B 18 0.292 777 Darrell Evans A E Det. 1B 18 0.251 535 Hal McRae A W K.C. DH 18 0.290 325 Rick Dempsey A E Cle. C 18 0.238 400 Steve Garvey N W S.D. 1B 18 0.295 1450 Ted Simmons N W Atl. UT 19 0.286 500 Graig Nettles N W Atl. 3B 20 0.249 200 Reggie Jackson A W Oak. DH 20 0.263 488 Pete Rose N W Cin. 1B 24 0.303 750

Explanation / Answer

a) we have to find mean, median and standard deviation for batting average of players.

Last second column is of batting average.

So we do it in excel by using following commands:

For mean : =AVERAGE( H2 : H 264)               (H is the column of batting average)

Median:   = MEDIAN (H2 : H 264)

Standard deviation: STDEVP (H2 : H 264) ( As it our population not sample)

After calculating we get

mean=

0.26320913

median=

0.263

std dev=

0.02333159

b) Histogram for the batting averages of players

first we create a column by side of the column of batting average that is bin ( in which we decide our class interval)

for this first we find minimum and maximum value with help of excel

min:      =MINIMUM( H2:H264)=0.196

max:     =MAXIMUM( H2:H264)=0.352

Then we get a range = 0.352-0.196=0.156

To make around 10 classes we have to make class width= 0.156/10=0.0156=0.016

Thus our bin will be:

0.196

0.212

0.228

0.244

0.26

0.276

0.292

0.308

0.324

0.34

0.356

command: DATA-> Data analysis->histogram->input range (H2:H264)->bin range (respective column)->click on chart output-> ok

then we get

Bin

Frequency

0.196

1

0.212

4

0.228

11

0.244

34

0.26

70

0.276

66

0.292

56

0.308

15

0.324

3

0.34

2

0.356

1

More

0

It means 0.276 batting average is most frequent.

c)

rookies

young

veteran

0.223

0.255

0.263

0.256

0.255

0.254

0.272

0.255

0.277

0.246

0.255

0.236

0.237

0.255

0.27

0.309

0.255

0.243

0.32

0.255

0.289

0.229

0.255

0.255

0.25

0.255

0.254

0.258

0.255

0.273

0.25

0.255

0.254

0.218

0.255

0.288

0.264

0.255

0.24

0.271

0.255

0.289

0.287

0.255

0.237

0.29

0.255

0.281

0.255

0.268

0.255

0.288

0.255

0.257

0.255

0.248

0.255

0.287

0.255

0.235

0.255

0.263

0.255

0.284

0.255

0.248

0.255

0.225

0.255

0.276

0.255

0.255

0.255

0.254

0.255

0.235

0.255

0.255

0.255

0.287

0.255

0.278

0.255

0.235

0.255

0.281

0.255

0.261

0.255

0.268

0.255

0.264

0.255

0.277

0.255

0.24

0.255

0.263

0.255

0.254

0.255

0.256

0.255

0.286

0.255

0.254

0.255

0.25

0.255

0.285

0.255

0.248

0.255

0.249

0.255

0.265

0.255

0.289

0.255

0.275

0.255

0.29

0.255

0.264

0.255

0.247

0.255

0.26

0.255

0.276

0.255

0.268

0.255

0.249

0.255

0.292

0.255

0.286

0.255

0.248

0.255

0.242

0.255

0.236

0.255

0.286

0.255

0.248

0.255

0.247

0.255

0.291

0.255

0.282

0.255

0.266

0.255

0.272

0.255

0.281

0.255

0.259

0.255

0.299

0.255

0.273

0.255

0.266

0.255

0.271

0.255

0.283

0.255

0.263

0.255

0.281

0.255

0.268

0.255

0.249

0.255

0.281

0.255

0.28

0.255

0.257

0.255

0.277

0.255

0.284

0.255

0.275

0.255

0.268

0.255

0.278

0.255

0.297

0.255

0.277

0.255

0.259

0.255

0.278

0.255

0.275

0.255

0.273

0.255

0.275

0.255

0.238

0.258

0.256

0.274

0.256

0.255

0.271

0.288

0.303

0.25

0.302

0.266

0.294

0.287

0.242

0.266

0.307

0.261

0.301

0.286

0.26

0.314

0.255

0.25

0.3

0.262

0.282

0.268

0.263

0.282

0.275

0.28

0.289

0.268

0.246

0.247

0.279

0.261

0.271

0.263

0.267

0.287

0.282

0.292

0.251

0.29

0.238

0.295

0.286

0.249

0.263

0.303

Command for quartile:

=QUARTILE(array: quart)       {quart=1 for Q1, quart=3 for Q3)

For Rorkies

min

0.218

Q1

0.24375

median

0.257

Q3

0.27575

max

0.32

For young

Min=Q1=median=Q3=max=0.255

For veteran

min

0.225

Q1

0.255

Median

0.268

Q3

0.282

Max

0.314

For all

min

0.218

Q1

0.255

median

0.255

Q3

0.2745

max

0.32

mean=

0.26320913

median=

0.263

std dev=

0.02333159

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