1. Math Research Project
By josh Caldwell

2. Manchester United FC One of the top clubs in England
Most premier league titles of any other club (20)
Record number of FA Cups (12) and FA Community Shields (21)
Coached by Jose Mourinho
Purchased Paul Pogba for a world-record 89.3 million £ ($116.4 m)

3. Players Annual Salaries
Weekly Salary (£)
Annual Salary (£)
Paul Pogba
290,000
15,080,000
Henrikh Mkhitaryan
140,000
7,280,000
Ashley Young
110,000
5,720,000
Anthony Martial
65,000
3,380,000
Antonio Valencia
70,000
3,640,000
Wayne Rooney
250,000
13,000,000
Zlatain Ibrahimovic
220,000
11,440,000
Memphis Depay
90,000
4,680,000
Marcus Rashford
20,000
1,040,000
Jesse Lingard
25,000
1,300,000
Juan Mata
Marouane Fellaini
80,000
4,160,000
Ander Herrera
75,000
3,900,000
Bastian Schweinsteiger
200,000
10,400,000
Morgan Schneiderlin 
100,000
5,200,000
Michael Carrick
Daley Blind
Player
Weekly Salary (£)
Annual Salary (£)
Luke Shaw
70,000
3,640,000
Timothy Fosu-Mensah
5,000
260,000
Eric Bailly
75,000
3,900,000
Chris Smalling
80,000
4,160,000
Phil Jones
50,000
2,600,000
Marcos Rojo
Sergio Romero
Matteo Darmian 
60,000
3,120,000
Sam Johnstone
10,000
520,000
David De Gea
200,000
10,400,000

4. Mean, Standard Deviation and Z-scores
The mean salary is £ ($ )
The standard deviation is ($  )
To calculate the Z-scores, we use the following formula :
In this case X = the annual salary

5. Five Favourite Players
Zlatan Ibrahimovic
Wayne Rooney
Paul Pogba
Marcus Rashford
Anthony Martial
Player
Salary
Z-Score
Ibrahimovic
11,440,000
1.67
Wayne Rooney
13,000,000
2.09
Paul Pogba
15,080,000
2.65
Marcus Rashford
1,040,000
-1.11
Anthony Martial
3,380,000
-0.49

6. Standard normal curve
Rooney
Rashford
Martial
Ibra Pogba

7. Their ranking by salary
1st 2nd 3rd 20th 25th
Paul Pogba
Wayne Rooney
Zlatan Ibrahimovic
Anthony Martial
Marcus Rashford

8. What do their Z-scores represent?
In this case, the Z-scores represent the number of standard deviations away from the mean.
For a higher z-score, the player receives more money annually.
If a z-score is negative, it means that the player earns less than the mean salary (5.2M)
Ranking

9. Factors that affect a players wages
- Transfer fee – Martial Vs Ibra
Performance – skill, goal contributions etc
Money available – Revenue per game
Demand – other clubs interest
Experience – Leadership, past performances
Productivity – 1 goal can be worth 10 million

10. Question 1 : What percentage of players are below the mean salary ?
The mean salary is £
There are 18 players below the mean salary
18/27 = 66.67%
Why does this happen?
The data is not normally distributed

11. Question 2 : What is the probability that someone’s salary is within 1 standard deviation of the mean?
5.2 M
There are 18 players that have a salary within 1 standard deviation of the mean, this is equal to %
Area = normalcdf ( , , , ) = … = %
Slightly off because data is not normally distributed

12. Average age of players outside one standard deviation of the mean
Below : Fosu-Mensah 19, Rashford 19, Johnstone 23, Lingard 24
Average age = years
Above : Pogba 23, De Gea 26, Zlatan 35, Rooney 31, Schweinsteiger 32
Average age = 29.4 years

13. Question 3 : How much would a player make to have a z-score of 3.00
3= 𝑥 −
=𝑥 − =𝑥

14. Sources
Manchester_United_have_revealed_that_their_new_signing_Pogba_wil-a-5_ jpg
Champions-League-group-stage.jpg
now/