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  • Level: GCSE
  • Subject: Maths
  • Word count: 3726

To compare the change in number of goals scored home and away by Premiership teams in two seasons. I will use the 2000-2001 and 2001-2002 seasons.

Extracts from this document...

Introduction

GOAL

Aim

To compare the change in number of goals scored home and away by Premiership teams in two seasons. I will use the 2000-2001 and 2001-2002 seasons.

Hypothesis (part 1)

I predict that the teams will score more goals at its home stadium than at the opposition’s stadium. This is because the players will be used to training and playing at their home stadium. They will not be as familiar with the opposition stadium. Also there will be more supporters for a home side at a home stadium so the players’ morale is boosted. These conditions also apply to the opposition. This means a team should score more at home than away.

I also predict that the teams, which tend to score more goals at home, will also score more goals away than the teams which score less at home. This is because these teams have a lot of good players who can adapt easier in foreign stadiums.

Investigation

I have created a table to show the number of goals scored by each team home and away in the 2000-2001season.

Team

Goals scored at Home

Goals scored Away

Manchester United

49

30

Arsenal

45

18

Liverpool

40

31

Leeds United

36

28

Ipswich Town

31

26

Chelsea

44

24

Sunderland

24

22

Aston Villa

27

19

Charlton Athletic

31

19

Southampton

27

13

Newcastle United

26

18

Tottenham Hotspurs

31

16

Leicester City

28

11

Middlesborough

18

26

West Ham United

24

21

Everton

29

16

Derby County

23

14

Manchester City

20

21

Coventry City

14

22

Bradford City

20

10

Total

587

405

It can be seen from the table that more goals are scored at home than away by the teams, 529 home goals as opposed to 405 away goals. Almost every team scored more goals at home than away. The only exceptions are Middlesborough and Coventry City.

Comparing Means

The mean of goals scored at home is 587 ÷ 20 = 29.35

...read more.

Middle

Manchester United

1

2

1

1

Arsenal

2

13

11

121

Liverpool

4

1

3

9

Leeds United

5

3

2

4

Ipswich Town

6

4

2

4

Chelsea

3

6

3

9

Sunderland

14

7

7

49

Aston Villa

11

11

0

0

Charlton Athletic

6

11

5

25

Southampton

11

18

7

49

Newcastle United

13

13

0

0

Tottenham Hotspurs

6

15

9

81

Leicester City

10

19

9

81

Middlesborough

19

4

15

225

West Ham United

14

9

5

25

Everton

9

15

6

36

Derby County

16

17

1

1

Manchester City

17

9

8

64

Coventry City

20

7

13

169

Bradford City

17

20

3

9

d2 = Difference squared

Σ = Total

Σ d2 = 962

R = 1 - (6 x Σ d2÷ n3 - n)

R = 1- (6 x 962 ÷ [203 – 20])

R = 0.28

This shows there is a weak positive correlation between the results. The correlation is not near enough to 1 to be of much use so cannot be followed up. This proves my second Hypothesis wrong.

Conclusion (part 1)

My first prediction was proved to be correct. Teams do tend to score more goals at home than away. This can be easily seen in the stem and leaf diagram. This is because the players will be used to training and playing at their home stadium. They will not be as familiar with the opposition stadium. Also there will be more supporters for a home side at a home stadium so the players’ morale is boosted. These conditions also apply to the opposition. This means a team should score more at home than away.

The only exceptions of this rule are Middlesborough and Coventry City. They have both scored more goals away. There are two possible reasons for this. One is that they may not train at their ground so are not as familiar with the home soil. The other is that their home stadiums are of a low quality so they play better away.

It can also be seen that the dispersion of goals scored away is smaller than that of goals scored at home. This is because the probability of the clubs scoring away is more similar.

I was wrong in saying the teams, which tend to score more goals at home, will also score more goals away than the teams which score less at home. Although there was a slight positive correlation, it was not strong enough to follow up.

Hypothesis (part 2)

To get a better conclusion I will repeat the investigation with information from the 2001 – 2002 season. I can then compare the results with that of the 2000 – 2001 season.

I predict that fewer goals will be scored at home matches and more goals will be scored at away matches. This is because clubs will have invested in better players and the quality of the current squad will have been improved. This means the clubs will be more similar, although there will still be some distance between the larger clubs, like Manchester United, and their smaller counterparts, like Derby County.

I predict the dispersion of home goals will be smaller. This is because the clubs have become increasingly similar in skill level. I predict the dispersion and range of away goals will be greater. This is because the clubs are playing better on other team’s pitches as a result from the similarity.

Even though there is all this, the number of home goals will still be greater than the number of away goals.

Investigation

I have created a table to show the number of goals scored by each team home and away in the 2001-2002 season.

Team

Goals scored at Home

Goals scored Away

Arsenal

42

37

Liverpool

33

34

Manchester United

40

47

Newcastle United

40

34

Leeds United

31

22

Chelsea

43

23

West Ham United

32

16

Aston Villa

22

24

Tottenham Hotspurs

32

17

Blackburn Rovers

33

22

Southampton

23

23

Middlesborough

23

12

Fulham

21

15

Charlton Athletic

23

15

Everton

26

19

Bolton Wanderers

20

24

Sunderland

18

11

Ipswich Town

20

21

Derby County

20

13

Leicester City

15

15

Total

557

444

Again the number of goals scored at home is greater than that scored away. It can also be seen that less goals are scored at home in comparison to the previous season. More goals are scored away in comparison to the previous season. Also a lot more teams have scored more away goals than home goals in comparison to the previous season. Liverpool, Manchester United, Aston Villa, Bolton wanderers and Ipswich town all scored more goals away than home.

Comparing Means

The mean of goals scored at home is 557 ÷ 20 = 27.85

The mean of goals scored away is 444 ÷ 20 = 22.20

This shows that the average team scores 6 (nearest whole number) more goals at home than it does away. This is 3 less goals than the season before. This shows that the scores of home and away matches are becoming more similar.

Using this mean the standard deviation can be found.

Standard deviation

Here is the standard deviation of the goals scored at home.

Team

Home Goals

Deviation

Squared Deviation

Arsenal

42

14.15

200.2

Liverpool

33

5.15

26.5

Manchester United

40

12.15

147.6

Newcastle United

40

12.15

147.6

Leeds United

31

3.15

9.9

Chelsea

43

15.15

229.5

West Ham United

32

4.15

17.2

Aston Villa

22

-5.85

34.2

Tottenham Hotspurs

32

4.15

17.2

Blackburn Rovers

33

5.15

26.5

Southampton

23

-4.85

23.5

Middlesborough

23

-4.85

23.5

Fulham

21

-6.85

46.9

Charlton Athletic

23

-4.85

23.5

Everton

26

-1.85

3.4

Bolton Wanderers

20

-7.85

61.6

Sunderland

18

-9.85

97.0

Ipswich Town

20

-7.85

61.6

Derby County

20

-7.85

61.6

Leicester City

15

-12.85

165.1

Total

557

1424.1

...read more.

Conclusion

I was correct in saying that fewer goals will be scored at home matches and more goals will be scored at away matches. This is because clubs will have invested in better players and the quality of the current squad will have been improved.

If the dispersion figures (range and standard deviation) are considered, then for the home matches they have decreased. For the away matches they have increased.

I was correct in stating the dispersion of home goals will be smaller. This is because the clubs have become increasingly similar in skill level. I predict the dispersion and range of away goals will be greater. This is because the clubs are playing better on other team’s pitches as a result from the similarity. After saying this there are still the elite teams at the top of the table (Arsenal, Liverpool and Manchester United) who will be near the top almost all the time.

Due to this increasing similarity, certain uniformity between the goals scored at home and those scored away has developed. This is shown by the weak positive correlation in from the first season becoming a strong positive correlation in the second. A team who scored more goals at home, will continue this trend away but not at such a great a scale.

If the statistics carry on as they do now, the number of away goals will equal the number of home goals. This means the best team will come first, the second best will come second and so on.

...read more.

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