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GCSE Maths Coursework: proportions of different parts of the body and thier relationship to height

Extracts from this document...

Introduction

image03.pngimage01.pngimage02.pngimage00.png


BOYS:

Rnd x Total

no. of samples

Sample no.

Sample no. (rounded to

nearest whole number)

THUMB

WRIST

NECK

WAIST

0.503*60

30.18

30

7

15

31.5

72

0.571*60

34.26

34

6

16.5

33

79

0.138*60

8.28

8

6

15

32

79

0.176*60

10.56

11

6.5

17.5

35

79

0.055*60

3.3

3

6.5

15

33

85

0.282*60

16.92

17

7

16

36

75

0.332*60

19.92

20

9

16.5

32

65

0.526*60

31.56

32

7

17.4

35

77

0.633*60

37.98

38

6

17

33

70

0.692*60

41.52

42

6

17

29

74

0.917*60

55.02

55

7

17.3

37

88.2

0.110*60

6.6

7

7

18

36

85

0.549*60

32.94

33

7

17.2

34

76

0.642*60

38.52

39

8

14.5

34.5

73

0.767*60

46.02

46

7

17

40.5

75.5

0.781*60

46.86

47

6.5

16.7

34

73

0.965*60

57.9

58

7.5

15.5

34

69

0.206*60

12.36

12

7

15

33

74

0.758*60

45.48

45

5.5

14

31

72

0.435*60

26.1

26

7

17

36.5

85.5

0.021*60

1.26

1

6.5

16

34

75

0.502*60

30.12

30

7

15

31.5

72

0.558*60

33.48

33

7

17.2

34

76

0.846*60

50.76

51

7.2

18.5

36

94.8

0.472*60

28.32

28

5.5

16

34

76

0.874*60

52.44

52

7.3

17

33.3

74

0.476*60

28.56

29

6.5

18

36

80

0.647*60

38.82

39

8

14.5

34.5

73

0.898*60

53.88

54

6.5

17

31

72.5

0.666*60

39.96

40

7

15.5

35

90

These are the 50% (30 samples out of 60) samples of boys data used in this investigation.


GIRLS:

Rnd x Total

no.

...read more.

Middle

0.784*80

62.72

63

6

14

31

75

0.053*80

4.24

4

6

16

33

77

0.222*80

17.76

18

6

15

30

60

0.122*80

9.76

10

6

15.5

31.5

70

0.809*80

64.72

65

6

16

32

67

0.607*80

48.56

49

6.5

16

30.5

71

0.982*80

78.56

79

6

14

30

67

0.599*80

47.92

48

6.5

16

31.1

73

0.797*80

63.76

64

7

15

31

61

0.350*80

28

28

5

15

29

61

0.719*80

57.52

58

6

16

32

73

0.241*80

19.28

19

6

15

31

68

0.563*80

45.04

45

5.7

15.5

32

72

0.966*80

77.28

77

6.5

16

30.5

66

0.238*80

19.04

19

6

15

31

68

0.492*80

39.36

39

6

15.5

31

69.5

0.322*80

25.76

26

7

16

33

64

0.418*80

33.44

33

6

15

32

79

0.631*80

50.48

50

6

14.5

30

65

0.529*80

42.32

42

6

14

26

69

0.181*80

14.48

14

6

16

41

69

0.164*80

13.12

13

5.5

15

41

68

0.772*80

61.76

62

5

14

28

69

These are the 50% (40 samples out of 80) samples of girls data used in this investigation.


‘They measure my right thumb and desired no more; for mathematical computation that twice round my thumb is once round the wrist and so on to the neck and waist.’

Aim:

To prove, through statistical analysis, if this statement is true

Planning:

The data that was used in this investigation was based on a random sample of both sexes aged 14-15 (Year 10).  Throughout the investigation there were two factors that were to be considered:

  1. Gulliver’s theory is based on adults, whereas we were using results of youngsters.  From birth to adulthood, children develop at varying rates and this could affect my results and alter my final outcome.
  2. Gulliver’s theory is based on that of someone with a perfectly proportioned body.  Different parts of the body do not develop at the same time, which will inevitably affect the results.

As we know males and females have different body shapes, so it would obviously be unfair to compare measurements of a female to that of a male, therefore I conducted two separate sets of results, female and male.

I was given a large amount of data and so I chose to take a random sample.  I only used 50% of the data provided and wanted to be sure that the 50% was selected at random with no particular trend in the selection process.  Through this method I was able to find the following results:

  1. Firstly I numbered the data provided (as it was given in the form of a list and each row needed to be numbered.).  I gave each individuals measurements a different number that I would refer to later in the sampling.
...read more.

Conclusion

- 0.457204

Moderate (+ve)

Wrist v Neck

- 0.400757

Moderate (+ve)

- 0.450033

Moderate (+ve)

Neck v Waist

- 0.466222

Moderate (+ve

- 0.189544

Weak (+ve)

Thumb v Waist

- 0.139840

Weak (-ve)

- 0.032060

Weak (-ve)

The final source of evidence that disproves this hypothesis is the gradients and intercepts of the lines of best fit in the particular graphs (with a 0.4 or above correlation).  

Table 5:

BOYS

GIRLS

Graph

Line of Best Fit Equation

Graph

Line of Best Fit Equation

Wrist V Neck

y = 0.7553x + 21.646

Thumb V Waist

y = 0.8602 + 10.019

Neck V Waist

y = 1.3815x + 30.043

Wrist V Neck

y = 1.6464 + 6.6133

If the relationship between each of the applications was double, as Gulliver stated, then I would expect there to be a gradient of 2 and it would be fair to say this was not the case with any of these relationships.  The equations of the lines of best fit are quite ridiculous in each graph and there is no evidence of a relationship between each of the characteristics.


Conclusion:

Although there seemed to be a slight relationship between the wrist and neck this is not enough to conclude that Gulliver’s theory is correct. Therefore on the basis of the data I used Gulliver’s theory is incorrect and I cannot accept this hypothesis to be true.

If I was to re-do this investigation then I would make the following improvements:

  • I would gain my samples from a larger number of people.  If I was calculating a mean over a greater amount of data then it would inevitable result in a more accurate, reliable mean.
  • Instead of collecting data from youngsters I would use samples from adults.  Youngsters have still not fully developed causing a variation throughout the data and between relationships.  Adults, on the other hand, are fully-grown and therefore provide more accurate results.
  • I would be sure to have just one person measuring the particular body parts so that all measurements are obtained through the same method and therefore resulting in a fairer investigation.  

GCSE Maths Coursework – Statistics (Gulliver’s Theory)

...read more.

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