Mini Case Study

Each year, Forbes Magazine presents rankings of World leading highest paid athletes, including lists of the oldest, youngest, women belonging to all types of games, highest paid celebrities, top 100 large companies, and top 100 small companies, etc.

In this case study, we discuss Forbes' list of 2015 of the highest paid athletics. The data includes their pay, salary per winnings, amount earned from endorsements, the type of the sports, and the number of big titles won (dummy and assumed variable and values). The list comprises of top 52 athletes with all the above mentioned information.

Required:

a)The table comprises of 7 different columns representing each variable. Identify the situation and nature of each variable. Identify, with which measurement scale the data of each variable belongs to? Justify your answer by giving one or two line reasons. (Means why or how qualitative/quantitative/discrete/continuousominal/ordinal/interval/ratio)

b)From whom point of view, this data could be treated as primary data? Secondary data? Give reasons for each.

c)Construct a frequency and relative frequency distribution of the variable "Sport". Represent the data through a suitable diagram. Comments/Interpret your diagram as well. Determine the modal sport category.

d)Construct a frequency, relative frequency, and cumulative (? and >) frequency distributions of the variable "# of Big Wins".

e)Draw a histogram for the frequency distribution in part (d). Make comments on the shape of the distribution.

f)Find and interpret the mean, median, and mode for the frequency distribution made in part (d). Determine its shape and compare it with the shape obtained in part (e). Comments on it.

g)Determine the variance, standard deviation, and coefficient of variation from the grouping done in part (d).

g)Detect the outliers in the data of "Salary/Winnings".

h)Select the variable "Endorsements", pick first 15 observations (keep the data ungroup) and find the coefficient of skewness and kurtosis and make a decision about the normality of the data.

Rank Name Pay Salary/ Winnings Endorsements Sport # of big Wins

#1 Floyd Mayweather

$300 M $285 M $15 M Boxing 10

#2 Manny Pacquiao

$160 M $148 M $12 M Boxing 8

#3 Cristiano Ronaldo

$79.6 M $52.6 M $27 M Soccer 5

#4 Lionel Messi

$73.8 M $51.8 M $22 M Soccer 7

#5 Roger Federer

$67 M $9 M $58 M Tennis 5

#6 LeBron James

$64.8 M $20.8 M $44 M Basketball 3

#7 Kevin Durant

$54.2 M $19.1 M $35 M Basketball 2

#8 Phil Mickelson

$50.8 M $2.8 M $48 M Golf 8

#9 Tiger Woods

$50.6 M $0.6 M $50 M Golf 6

#10 Kobe Bryant

$49.5 M $23.5 M $26 M Basketball 4

#11 Ben Roethlisberger

$48.9 M $46.4 M $2.5 M Football 7

#12 Rory McIlroy

$48.3 M $16.3 M $32 M Golf 6

#13 Novak Djokovic

$48 M $17.2 M $31 M Tennis 3

#14 Zlatan Ibrahimovic

$39.1 M $33.1 M $6 M Soccer 1

#15 Lewis Hamilton

$39 M $36 M $3 M Racing 2

#16 Ndamukong Suh

$38.6 M $38.2 M $0.4 M Football 2

#17 Fernando Alonso

$35.5 M $34 M $1.5 M Racing 8

#18 Gareth Bale

$35 M $25.5 M $9.5 M Soccer 10

#19 Jon Lester

$34.1 M $33.7 M $0.4 M Baseball 9

#20 Derrick Rose

$33.9 M $18.9 M $15 M Basketball 1

#21 Sebastian Vettel

$33 M $32 M $1 M Racing 8

#22 Rafael Nadal

$32.5 M $4.5 M $28 M Tennis 2

#23 Mahendra Singh Dhoni

$31 M $4 M $27 M Cricket 7

#23 Neymar

$31 M $14 M $17 M Soccer 7

#25 Carmelo Anthony

$30.5 M $22.5 M $8 M Basketball 3

#26 Maria Sharapova

$29.7 M $6.7 M $23 M Tennis 6

#27 Carson Palmer

$29 M $28.5 M $0.5 M Football 3

#27 James Rodriguez

$29 M $24.5 M $4.5 M Soccer 5

#29 J.J. Watt

$27.9 M $20.9 M $7 M Football 6

#30 Robinson Cano

$27.6 M $24.1 M $3.5 M Baseball 2

#31 Dwyane Wade

$27.2 M $15.2 M $12 M Basketball 5

#32 Peyton Manning

$27 M $15 M $12 M Football 4

#32 Kimi Raikkonen

$27 M $25 M $2 M Racing 6

#34 Clayton Kershaw

$26.9 M $25.7 M $1.2 M Baseball 8

#34 Wayne Rooney

$26.9 M $19.9 M $7 M Soccer 9

#36 Gerald McCoy

$26.7 M $26.5 M $0.15 M Football 7

#37 Chris Paul

$26.1 M $20.1 M $6 M Basketball 10

#38 Radamel Falcao

$25.9 M $21.9 M $4 M Soccer 10

#38 Albert Pujols

$25.9 M $23.4 M $2.5 M Baseball 8

#40 Ryan Howard

$25.6 M $25 M $0.6 M Baseball 8

#41 Dwight Howard

$25.5 M $21.5 M $4 M Basketball 7

#42 Cliff Lee

$25.2 M $25 M $0.2 M Baseball 7

#43 Miguel Cabrera

$25.1 M $22.1 M $3 M Baseball 4

#44 Amar'e Stoudemire

$25 M $22 M $3 M Basketball 4

#45 Blake Griffin

$24.7 M $17.7 M $7 M Basketball 5

#46 Serena Williams

$24.6 M $11.6 M $13 M Tennis 6

#47 Prince Fielder

$24.3 M $24 M $0.3 M Baseball 9

#48 Joe Johnson

$24.2 M $23.2 M $1 M Basketball 3

#49 Joe Mauer

$24 M $23 M $1 M Baseball 2

#50 CC Sabathia

$23.9 M $23 M $0.9 M Baseball 1

#51 Chris Bosh

$23.8 M $20.8 M $3 M Basketball 8

#52 Zack Greinke

$23.7 M $23.7 M $0.05 M Baseball 6

Shapes SmartArt Chart Screenshot|Hyperlink Bookmark Cross-reference Header Footer Page Illustrations Number Text Quick WordArt Drop Big Date & Time Links Box . Parts - Header & Footer Cap- Object . Equation Symbol Text Rank Name Pay Salary/ Winnings Endorsements Sport # of big Wins #1 Floyd Mayweather $300 M $285 M $15 M Boxing 10 #2 Manny Pacquiao $160 M $148 M $12 M Boxing 8 #3 Cristiano Ronaldo $79.6 M $52.6 M $27 M Soccer 5 #4 Lionel Messi $73.8 M $51.8 M $22 M Soccer 7 #5 Roger Federer $67 M $9 M $58 M Tennis 5 #6 LeBron James $64.8 M $20.8 M $44 M Basketball 3 #7 Kevin Durant $54.2 M $19.1 M $35 M Basketball 2 #8 Phil Mickelson $50.8 M $2.8 M $48 M Golf 8 #9 Tiger Woods $50.6 M $0.6 M $50 M Golf 6 #10 Kobe Bryant $49.5 M $23 5 M $26 M Basketball 4 #11 Ben Roethlisberger $48.9 $46.4 M $2.5 M Football 7 #12 Rory Mcilroy $48 3 $16.3 M $32 M Golf 6 $17 2 M 3 #13 Novak Djokovic $48 M $31 M Tennis #14 Zlatan Ibrahimovic $39.1 M $33.1 M $6 M Soccer #15 Lewis Hamilton $39 M $36 M $3 M Racing 2 #16 Ndamukong Suh $38.6 M $38.2 M $0.4 M Football 2 $34 M $1.5 M Racing 8 #17 Fernando Alonso $35.5 Mture Clip Signature Line . Art Shapes SmartArt Chart Screenshot| Hyperlink Bookmark Cross-reference | Header Footer Page Text Quick WordArt Drop To Date Is Time Blustrations Number Links Box - Parts . Header & Footer Cap - Object #18 Gareth Bale $35 M $25.5 M $9.5 M Soccer 10 #19 Jon Lester $34.1 M $33.7 M $0.4 M Baseball 9 #20 Derrick Rose $33.9 M $18.9 M $15 M Basketball #21 Sebastian Vettel $33 M $32 M $1 M Racing 8 #22 Rafael Nadal $32.5 M $4.5 M $28 M Tennis 2 #23 Mahendra Singh Dhoni $31 M $4 M $27 M Cricket 7 #23 Neymar $31 M $14 M $17 M Soccer 7 #25 Carmelo Anthony $30.5 M $22.5 M $8 M Basketball 3 #26 Maria Sharapova $29.7 M $6.7 M $23 M Tennis 6 #27 Carson Palmer $29 M $28.5 M $0.5 M Football LO #27 James Rodriguez $29 M $24.5 M $4.5 M Soccer #29 J.J. Watt $279 M $20.9 M $7 M Football 6 #30 Robinson Cano $24.1 M $3.5 M Baseball 2 Dwyane Wade $27.2 M $15.2 M $12 M Basketball #31 Peyton Manning $27 M $12 M Football #32 $15 M $25 M Racing 6 #32 Kimi Raikkonen $27 M $2 MClip A Shapes SmartArt Chart Screenshot | Hyperlink Bookmark Cross-reference Signature Line . Art Header Footer Page Text In Date for Time IC S2 Mustrations Links Number * Quick WordArt Drop Box - Parts - Cap -Objed - Equation Symbol Header & Footer #32 Kimi Raikkonen Text $27 M $25 M $2 M 6 #34 Racing Clayton Kershaw $26.9 M $25.7 M $1.2 M Baseball 8 #34 Wayne Rooney $26.9 M $19.9 M $7 M Soccer 9 #36 Gerald Mccoy $26.7 M $26.5 M $0.15 M Football 7 #37 Chris Paul $26.1 M $20.1 M $6 M Basketball 10 #38 Radamel Falcao $25.9 M $21.9 M $4 M Soccer 10 #38 Albert Pujols $25.9 M $23.4 M $2.5 M Baseball 8 #40 Ryan Howard $25.6 M $25 M $0.6 M Baseball #41 Dwight Howard $25.5 M $21.5 M $4 M Basketball 7 #42 Cliff Lee $25.2 M $25 M $0.2 M Baseball 7 #43 Miguel Cabrera $25.1 M $22.1 M $3 M Baseball 4 #44 Amar'e Stoudemire $25 M $22 M $3 M Basketball 4 #45 Blake Griffin $24.7 M $17.7 M $7 M Basketball 5 #46 Serena Williams $24.6 M $116 M $13 M Tennis 6 9 #47 Prince Fielder $24 $24 M $0.3 M Baseball #48 Joe Johnson $24 $23.2 M $1 M Basketball 3 #49 Joe Mauer $24 M $23 M $1 M Baseball CC Sabathia $23.9 M $23 M $0.9 M Baseball #50 $23.8 M $20.8 M Basketball Chris Bosh $3 M 8 #51 $23.7 M $0.05 M Baseball 6 #52 Zack Greinke $23.7 M Po W