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This Investigation is to see if there is a correlational relationship between individuals G.C.S.E grades and their AS-Level grades, hence also individuals ability to adapt to a higher volume of more difficult study.

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Introduction

Maths Coursework - Statistics

Aims

This Investigation is to see if there is a correlational relationship between individuals G.C.S.E grades and their AS-Level grades, hence also individuals ability to adapt to a higher volume of more difficult study. This is a particularly relevant area to research as I am currently studying at Sir John Deanes College in Northwich. I am interested in seeing how well individuals do at a higher level of education, when they are often under a higher degree of pressure due to other aspects of life.

Data Collection

In this investigation the population is the students who attend Sir John Deanes College in Northwich. As this is a large college a sampling method clearly needs to be used. When I originally collected my data I obtained information from two Art classes, two Maths classes and two English classes, in effort to obtained results from students who excelled in different academic areas. Once this data was obtained I stratified these 66 results into 50 results, representative of the number of participants originally sampled.

Sampling

50 Participants data needed from the original 66 obtained, the sum to calculate how many of each were needed is:

(Subject total/Overall total)*50

No. Needed

English

18

Maths

18

Art

14.3

N.B.

...read more.

Middle

Maths

Female

3.8

3.4

28

Maths

Female

3.75

3.4

29

Maths

Female

3.9

4.25

30

Maths

Male

4.6

1.4

31

Maths

Male

3.36

2

32

Maths

Female

4.8

3

33

Maths

Female

5.6

4.8

34

Maths

Female

4.25

1

35

Maths

Male

4.2

2.2

36

Maths

Female

3.55

4

37

Art

Male

4.5

4

38

Art

Female

3.75

3.6

39

Art

Female

3.3

1.5

40

Art

Female

3.38

2.75

41

Art

Female

5

3.6

42

Art

Female

5.1

4.5

43

Art

Female

3.3

2.75

44

Art

Female

4.2

3

45

Art

Male

5.6

5

46

Art

Male

4.6

3

47

Art

Male

3.5

2.4

48

Art

Male

4.18

3.4

49

Art

Male

4.9

3.8

50

Art

Male

4.9

4.4

Above is the data after sampling had taken place. This data was put in a scatter graph using a program called Autograph®, and a line of best fit was also drawn to help illustrate the linear relationship between the two random variables, This can be seen below:

image00.png

The above scatter graph indicates an approximate elliptical shape as well as linear relationship. Both of the variables are also random. Therefore I will use Pearson’s Product Moment Correlation Coefficient (P.P.M.C.C.) which will indicate the strength of the relationship, allowing me to formulate a hypothesis test to see if this relationship is significant, using critical values.

Shown Below is the Calculations done to find out the correlation coefficient for this data:

GCSE(x)

AS (y)

(x-mean x)

...read more.

Conclusion

        Another flaw in this investigation is that it focuses on only students from three subject areas: Maths, English and Art. It is clear this is not representative of the entire population of students and doesn’t collect a broad enough set of data to give results that can be generalised. To counter this problem participants from a broader range of subjects would need to be sampled, this would allow the results to be much more representative.

 The data used in this sample was exclusively from students at Sir John Deane’s College in Northwich, a centre of excellence which has high entry grades (B grades at G.C.S.E.) therefore again the results show only a section of the relationship between the two levels of education. This means that results cannot be generalised to a wider population. To help stop this problem the investigation would have to take samples from students at different colleges with varying entry requirements to give conclusions that could be more easily generalised.

...read more.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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