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  • Level: GCSE
  • Subject: Maths
  • Word count: 2378

Investigating the relationship between height and weight for the pupils in a secondary school.

Extracts from this document...

Introduction

AS Level Statistics Project

Investigating the relationship between height and weight for the pupils in a secondary school


Table of Contents

Introduction

Primary Data by Direct Observation

Secondary Data

Hypotheses

1. Distribution

2. Comparative

Methods

Data Collection

Choosing the Data

Stratified Sampling

Randomised Selection

Analysis and Interpretation of Data

Data Summaries

Measures of Spread of Data

Box and Whisker Diagrams

Stem and leaf and Frequency Table (Boys Height)

Stem and leaf and Frequency Table (Girls Height)

Stem and leaf and Frequency Table (Boys Weight)

Stem and leaf and Frequency Table (Girls Weight)

Standard deviation and confidence intervals

Comparing heights against Weight for Boys

Correlation Analysis

Comparing heights against Weight for Girls

Correlation Analysis

Conclusions

Evaluation

Appendix 1 – The data


Introduction

For this investigation, I am going to use data on secondary school pupils to find the distribution of the data and also to look for any meaningful relationships between the heights and weights of the students.  

When I was looking at the various things that I could study, one of the factors that I looked at was data collection.

The amount of data was large, spanning across different year groups.  I could have looked at the variation of weight and height with age and with gender, but this would have made the project too long and time-consuming.

...read more.

Middle

35

40

45

50

55

60

65

70

75

80

85

image03.png

35

40

45

50

55

60

65

70

75

80

85

A comparison of the Box Plots for Boys and Girls’ weight indicates that whilst there is a greater spread amongst the girls, the distributions are more comparable than with the heights.


Stem and leaf and Frequency Table (Boys Height)

Stem

Leaf

Range

Midpoint

Frequency

1.3

5 6

1.3 ≤ H< 1.4

1.35

2

1.4

5 9

1.4 ≤ H< 1.5

1.45

2

1.5

0 0 0 1 2 3 3 5 6 7 7 7 8 9 9 9 9 9

1.5 ≤ H< 1.6

1.55

18

1.6

0 0 0 1 1 2 2 2 2 2 2 3 4 4 5 5 7 9

1.6 ≤ H< 1.7

1.65

18

1.7

0 1 5

1.7 ≤ H< 1.8

1.75

3

1.8

0

1.8 ≤ H< 1.9

1.85

1

This distribution can be seen more easily by drawing a graph:

image04.png

From the look of this graph, it can be assumed that the distribution of boys’ heights is ‘normal’.


Stem and leaf and Frequency Table (Girls Height)

Stem

Leaf

Range

Midpoint

Frequency

1.3

-

1.3 ≤ H< 1.4

1.35

0

1.4

6 7

1.4 ≤ H< 1.5

1.45

2

1.5

0 2 2 3 4 4 4 5 5 5 6 8

1.5 ≤ H< 1.6

1.55

12

1.6

0 0 1 1 2 5 5 6 6 7 7

1.6 ≤ H< 1.7

1.65

11

1.7

0 1 3 3 5 5 5 7

1.7 ≤ H< 1.8

1.75

8

1.8

0 0 0

1.8 ≤ H< 1.9

1.85

3

This distribution can be seen more easily by drawing a graph:

image05.png

From the look of this graph, it can be assumed that the distribution of girls’ heights is skewed.  The skew is much more noticeable from this graph than from Box Plots.


Stem and leaf and Frequency Table (Boys Weight)

Stem

Leaf

Range

Midpoint

Frequency

3

8

30 ≤ H< 40

35

1

4

0 2 2 4 5 5 5 5 7 8

40 ≤ H< 50

45

10

5

0 0 1 1 2 2 2 4 4 4 8

50 ≤ H< 60

55

11

6

0 0 0 0 0 3 4 5 6 6

60 ≤ H< 70

65

10

7

0 0 5

70 ≤ H< 80

75

3

8

5

80 ≤ H< 90

85

1

This distribution can be seen more easily by drawing a graph:

image06.png

This graph looks slightly skewed, but there are too few data at the periphery of the distribution to be sure.


Stem and leaf and Frequency Table (Girls Weight)

Stem

Leaf

Range

Midpoint

Frequency

3

6 7 8 8

30 ≤ H< 40

35

4

4

0 2 2 2 5 6 6 6 7 8 8 8 8 8 8 8 8

40 ≤ H< 50

45

17

5

0 0 1 1 1 2 2 2 2 2 4 4 4 5 5 7 7 8 8

50 ≤ H< 60

55

19

6

2 5 5 5

60 ≤ H< 70

65

4

7

-

70 ≤ H< 80

75

8

-

80 ≤ H< 90

85

This distribution can be seen more easily by drawing a graph:

image07.png

From the look of this graph, it can be assumed that the distribution of boys’ weights is ‘normal’ since a single data point moving from the 55 to 45 would make the distribution symmetrical.


Standard deviation and confidence intervals

Statistic

Boys Height (m)

Boys Weight (Kg)

Girls Height (m)

Girls Weight (Kg)

Mean

1.59

50.02

1.63

55.08

Standard Deviation (SD)

0.10

10.65

0.086

7.19

...read more.

Conclusion

This was also shown not to be true.

Hypothesis 2.c.  

As the height increases, the weights will increase in proportion.

Although there seems to be a slight linear relationship, there is too much variability in the data and for boys, only 15% of the variability can be attributed to the variability in weight can be attributed to height and for girls, this becomes even less at almost 4%.

Evaluation

Overall, the results for the comparison of heights and weights were surprising.  I expected to see a much greater relationship between height and weight and a greater difference between boys and girls.

However, the distributions were as I expected.

If I were to do this project again, I would do the analysis taking account of the outliers.


Appendix 1 – The data

Girls

Boys

Name

Height (m)

Weight (kg)

Name

Height (m)

Weight (kg)

Gemma

1.65

54

Herman

1.60

60

Ashley

1.65

48

Mahmood

1.56

60

Kathleen

1.7

52

Hosaib

1.66

54

Natalie

1.5

45

Hosiab

1.66

70

Hannah

1.62

52

Matthew

1.52

52

Amna

1.35

51

Khuram

1.75

75

Sonia

1.67

48

Pauya

1.65

45

Holly

1.63

47

Kurt

1.52

54

Rachael

1.56

50

Vintchenzo

1.67

54

Rachael

1.45

51

Albert

1.71

60

veronica

1.49

37

Steve

1.80

48

Victoria

1.75

65

Robin

1.73

66

Samantha

1.62

48

Stanley

1.55

50

Louise

1.51

48

Wayne

1.77

66

Tahira

1.62

42

Gary

1.73

52

Humspira

1.69

48

Jake

1.54

44

Nichola

1.36

38

Jon

1.47

42

Carol

1.58

55

Anthony

1.75

63

Ben

1.8

57

Andrew

1.62

40

Farrah

1.59

42

Andrew

1.46

45

Suzanne

1.6

46

John

1.80

64

Janine

1.62

54

Bob

1.50

70

Karen

1.6

46

Michael

1.61

38

Channan

1.59

52

Simon

1.54

60

Julie

1.59

50

Daniel

1.55

51

Stacey

1.55

57

James

1.54

42

Charelle

1.61

52

Jamie

1.80

51

Nichole

1.57

62

John

1.67

52

Rosie

1.5

65

Azhar

1.55

47

Suki

1.52

52

Jimmy

1.61

45

Louise

1.59

46

Tyler

1.70

85

Nicola

1.62

48

Tommas

1.58

65

Rose

1.61

38

John

1.60

58

Christine

1.64

42

William

1.65

50

Jade

1.57

48

Paul

1.53

45

Sarah

1.53

40

Simon

1.75

60

Caroline

1.59

48

Sandra

1.64

55

Louise

1.62

58

Amy

1.5

65

Kaylea

1.6

51

Samantha

1.71

54

Grebla

1.57

36

Belinda

1.53

58

...read more.

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