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  • Level: GCSE
  • Subject: Maths
  • Word count: 4581

My hypotheses are: -1. People's average SAT and average GCSE results will have a strong positive correlation between them.2. Girl's average GCSE result will generally be higher than boy's average GCSE result.

Extracts from this document...

Introduction

The Plan

My hypotheses are: -

  1. People’s average SAT and average GCSE results will have a strong positive correlation between them.
  2. Girl’s average GCSE result will generally be higher than boy’s average GCSE result.

All the data used will be from Steel City School

 For both of my hypotheses I am going to use a sample of 55 people. For my sampling I am first going to use stratified sampling, when I have a number of people I am going to role a dice to decide where I start. I believe that the minimum number of people that should be sampled is 50. 50 out of the 166 pieces of data is 30% and 55 out of 166 is 33%. With only 30 pieces of data in my sample I believe that I may not get a good spread of both boys and girls results. With a sample of 55 I believe that I will get a fair sample and a large spread of both boys and girls.

I intend to show the data on a series of graphs. For my first hypothesis “People’s average SAT and average GCSE results will have a strong positive correlation between them.” I am going to use three scatter graphs. The first graph will be a scatter graph showing only boys average SAT and GCSE results. The second graph will be a scatter graph showing only girls average SAT and GCSE results.

...read more.

Middle

5.5

30.25

6.67

6.8

3

4

1

1

6

5.45

17.5

21

3.5

12.25

5

4.5

27.5

29

1.5

2.25

6.33

6.25

11

10

1

1

6.33

6.55

11

7

4

16

6.67

6.6

3

6

3

9

6.33

6.15

11

11.5

0.5

0.25

5

5.45

27.5

21

5.5

30.25

5.67

6.4

22.5

8

14.5

210.25

5.33

4.85

26

27

1

1

6.33

5.25

11

24

13

169

6

5.15

17.5

25

7.5

56.25

6.33

5.91

11

15

4

16

4.67

5.45

29

21

8

64

5.33

6.15

26

11.5

14.5

210.25

6

6

17.5

14

3.5

12.25

3.67

4.1

30

30

0

0

5.67

5.45

22.5

21

0.5

0.25

6.67

6.05

3

13

10

100

6.33

7.2

11

3

8

64

5.33

4.78

26

28

2

4

6.33

7.25

11

2

9

81

6.33

5.5

11

18

7

49

5.67

5.09

22.5

26

3.5

12.25

6

6.27

17.5

9

8.5

72.25

1385

Using Spearmans Co-efficient of Rank Correlation I have found out that there is a fairly strong correlation between girls average GCSE results and girls average SAT results. The strongest positive correlation is 1 and the results above show that in this case the correlation is 0.69, which is fairly strong. The correlation is smaller than both the boys and the combined boys and girls average results.

Boys and girls

SAT’s average

GCSE average

SAT Rank

GCSE Rank

Difference

Difference²

4.33

3.2

50.5

52

1.5

2.25

2.67

1.28

55

55

0

0

6.33

6.64

13.6

10

3.6

12.96

5.67

4.75

31

40

9

81

5.33

4.4

38.5

43

4.5

20.25

5.67

4.6

31

41

10

100

6

5.35

23.5

33

9.5

90.25

6.67

6.8

6

6.5

0.5

0.25

5

4.25

44

45

1

1

6.67

5.79

6

21

15

225

5.67

4.35

31

33

2

4

4

3.64

52

50

2

4

5.33

5.5

38.5

26.5

12

144

4.33

3.7

50.5

49

1.5

2.25

5.67

5.63

31

24

7

49

5.33

5.65

38.5

23

15.5

240.25

4.67

3.05

48

53

5

25

7

7.2

2.5

3.5

1

1

5.67

3.9

31

47

16

256

5

5.22

44

35

9

81

6

6.65

23.5

9

14.5

210.25

3

2.7

54

54

0

0

5

3.8

44

48

4

16

7

6.95

2.5

5

2.5

6.25

4.67

3.6

48

51

3

9

6.33

5.45

13.6

30

16.4

268.96

7.33

7.59

1

1

0

0

6.33

6.77

13.6

8

5.6

31.36

6.33

5.75

16.3

22

5.7

32.49

5.67

5.6

31

25

6

36

6.67

6.8

6

6.5

0.5

0.25

6

5.45

23.5

30

6.5

42.25

5

4.5

44

42

2

4

6.33

6.25

13.6

15

1.4

1.96

6.33

6.55

13.6

12

1.6

2.56

6.67

6.6

6

11

5

25

6.33

6.15

13.6

16.5

2.9

8.41

5

5.45

44

30

14

196

5.67

6.4

31

13

18

324

5.33

4.85

38.5

38

0.5

0.25

6.33

5.25

13.6

34

20.4

416.16

6

5.15

23.5

36

12.5

156.25

6.33

5.91

13.6

20

6.4

40.96

4.67

5.45

48

30

18

324

5.33

6.15

38.5

16.5

22

484

6

6

23.5

19

4.5

20.25

3.67

4.1

53

46

7

49

5.67

5.45

31

30

1

1

6.67

6.05

6

18

12

144

6.33

7.2

13.6

3.5

10.1

102.01

5.33

4.78

38.5

39

0.5

0.25

6.33

7.25

13.6

2

11.6

134.56

6.33

5.5

13.6

26.5

12.9

166.41

5.67

5.09

31

37

6

36

6

6.27

23.5

14

9.5

90.25

3491.82

...read more.

Conclusion

Cumulative Frequency

Looking at my cumulative frequency graph for boys I can see that there is a large spread of data. There appears to be a very slight negative skew on the box plot. Looking at the box plot I can see that the four-quarters of data is very evenly distributed. Looking at the cumulative frequency graph for girls I can see that it is very different to the boys. Firstly the spread of data is very small but the spread seems to be at a higher point on the graph compared to the boys. Looking at the box plots I can see that there is a slightly positive skew and that the highest quarter of people seem to get higher grades (6.5 – 8).

Pie Chart

Again looking at my three pie charts I can see that a higher amount of girls attained higher average levels compared to the boys. This tends to agree with what my other graphs have also proven. Looking at the boys and girls pie chart I can see that the majority of boys and girls got a average level between five and seven.

Philip Jacobs 10R GCSE Math’s Data Handling

...read more.

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