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  • Level: GCSE
  • Subject: Maths
  • Word count: 4571

Data handling investigating height and weight.

Extracts from this document...

Introduction

Data Handling Coursework

For my data handling coursework I will be investigating Height and Weight.  I will also be investigating how gender and age affect these.  I need to collect information on Height, Weight, Age and Gender.  The information I am using has been collected by a secondary source so the data should be accurate.  I can foresee that, I could have a problem with data if it’s incorrect, so, if I get any incorrect data I will ignore it.

The following table shows information about the number of boys and girls in each year at Mayfield High School.

Year Group

Number of Boys

Number of Girls

Total

7

151

131

282

8

145

125

270

9

118

143

261

10

106

94

200

11

84

86

170

1183

Hypotheses

  1. My first hypothesis is: There will be a positive correlation between height and weight.
  1. My second hypothesis is: Is Height affected by age and gender.
  1. My third hypothesis is: Does body mass index change for different years and genders.

Hypothesis 1

To test this hypothesis I will firstly collect a random sample of 100 students.  To collect this random sample I will use my calculator: I will use the random number generator and then multiply it by 1183, the number I get will be a number of a pupil.  If the calculator selects a number that I have already chosen I will ignore it.

The Data: Here is the random sample of 100 students from the school

Height

Weight

Height

Weight

Height

Weight

Height

Weight

1.58

45

1.52

47

1.92

45

1.48

34

1.70

45

1.69

65

1.52

54

1.47

44

1.59

49

2.00

86

1.58

50

1.62

50

1.54

42

1.53

48

1.50

65

1.70

55

1.50

47

1.55

65

1.96

93

1.62

40

1.64

44

1.90

40

1.75

56

1.50

45

1.53

40

1.56

74

1.62

54

1.59

44

1.54

45

1.50

40

1.83

60

1.25

35

1.59

45

1.50

39

1.73

50

1.74

47

1.67

66

1.52

38

1.59

52

1.55

50

1.70

60

1.30

35

1.55

47

1.44

42

1.67

57

1.57

40

1.70

57

1.68

40

1.54

45

1.68

54

1.52

37

1.75

63

1.39

42

1.73

64

1.41

31

1.66

46

1.59

44

1.63

45

1.60

38

1.60

47

1.63

48

1.65

68

1.62

40

1.73

50

1.55

60

1.66

70

1.46

45

1.57

54

1.59

45

1.65

40

1.82

66

1.62

56

1.41

39

1.45

31

1.74

80

1.81

54

1.51

40

1.83

64

1.43

41

1.72

51

1.57

56

1.54

60

1.49

67

1.60

60

1.69

48

1.75

60

1.74

70

1.75

80

1.48

44

1.56

60

1.63

42

1.72

57

1.69

48

1.72

54

1.63

55

1.55

45

1.70

50

1.67

66

1.70

51

1.51

50

Now I have collected the random sample I can find out if the correlation between height and weight is positive or negative.

...read more.

Middle

Female

1.65

11

Male

1.83

11

Female

1.72

11

Male

1.8

11

Female

1.60

11

Male

1.76

11

Female

1.56

First of all I am going present each of the groups on a stem and leaf diagram to show the most common heights for each age group.

Year 7

Stem

Leaf

Frequency

130

6

1

140

1,3,3,5,6,7,8,8,9

9

150

1,2,2,2,3,5,5,6,8,9

10

160

2,2,2,2,4,5,5

7

170

0,4

2

180

0

1

Year 9

Stem

Leaf

Frequency

130

5

1

140

5,6

2

150

0,0,1,2,2,3,3,4,8

9

160

0,2,2,3,4,5,5,6,7

9

170

0,0,1,1,5,6

6

180

0,2,5

3

Year 11

Stem

Leaf

Frequency

150

0,5,6,6,7,8

6

160

0,1,1,2,2,2,3,3,4,5,8,8

14

170

0,2,3,6

4

180

0,1,3,3,4

5

190

7

1

The stem and leaf diagram shows that the most common height for year 7 is between 150cm and up to but not including 160cm.  For year 9 it shows the most common height is between 150cm and up to but not including 170cm.  For year 11 the most common height is between 160cm and up to but not including 170cm.  This shows that the most common height group of year 11 is taller than year 7 and 9.  Also the diagrams show that year 11 stem starts at a higher height than the other years, this shows that year 11 smallest pupil is taller than year 9 and 7 smallest pupil so this shows that yr11 are taller.  

So, these diagrams show that Height is effected by age, and that the older you are the taller you are, but they do not show if height is affected by gender.  To find out if Height is affected by gender I am going to firstly need to show the data of boys and girls on separate cumulative frequency diagrams.

Totals

Cumulative Frequency

Height (cm)

Boys

Girls

Mixed

Boys

Girls

Mixed

<130

1

1

2

1

1

2

<140

4

7

11

5

8

13

<150

8

17

25

13

25

38

<160

15

14

29

28

39

67

<170

10

3

13

38

42

80

<180

6

3

9

44

45

89

<190

1

0

1

45

45

90

The cumulative frequency curves above show that most girls’ heights tend to be lower than the boy’s heights.  It also shows that the girls curve starts to go up more steeply after 150cm where as the boys starts to go up more steeply at about 160cm this shows that most boys heights are above a higher amount than the girls.  I can use the cumulative frequency curves to work out how many percent of the boys in the school are over 1.6m and below 1.8m and how many percent of girls are in this range.image15.pngimage05.png

The cumulative frequency table tells me that there are 25 boys between 1.60m and 1.80m and there are 17 girls between 1.60m and 1.80m.

So this means that 25/90= 5/18 or 28% of the boys in the school will be between 1.60m and 1.80m and 17/90 or 19% of the girls in the school will be between 1.60m and 1.80m.  This means that if I selected a boy at random from the school then there is a 0.28 chance of him been between 1.60m and 1.80m.  Also because the percentage of girls in these ranges is lower than the boys it suggests that boys are in general taller than the girls.

image16.pngThe box plots show that the boy’s heights are a lot more spread out than the girls.  They also show that the boys average height is outside of the interquartile range of the girls, this shows that over 75% of the girls in my sample are smaller than the boys average height.image06.png

I have come to the conclusion, that the evidence shows, that the older you are the taller you are likely to be and if you are male you are likely to be taller than a female.  So the answer to the Hypothesis “Is height effected by age and gender” is yes it is.

Hypothesis 3

To test this hypothesis, which is, does body mass index change for different years and genders I will be using the stratified sample I used for my second hypothesis.

Body Mass Index (BMI) is your weight in kilograms divided by your height in meters squared: BMI=Kg/m2.  Body Mass Index can be used to indicate if you are overweight, underweight or normal when.  It can also show the average weight that other people of your Age, Height, Weight and Gender are.  

First of all I am going to turn the results of the stratified sample into body mass index.

Year

Gender

Height (m)

Weight (kg)

BMI kg/m2

Year

Gender

Height (m)

Weight (kg)

BMI kg/m2

7

Male

1.65

41

15.06

7

Female

1.53

47

20.08

7

Male

1.55

45

18.73

7

Female

1.46

40

18.77

7

Male

1.62

45

17.15

7

Female

1.48

34

15.52

7

Male

1.58

57

22.83

7

Female

1.47

44

20.36

7

Male

1.65

69

25.34

7

Female

1.62

50

19.05

7

Male

1.62

47

17.91

7

Female

1.62

40

15.24

7

Male

1.36

38

20.54

7

Female

1.51

50

21.93

7

Male

1.52

54

23.37

7

Female

1.43

45

22.01

7

Male

1.59

52

20.57

7

Female

1.64

47

17.47

7

Male

1.55

47

19.56

7

Female

1.80

110

33.95

7

Male

1.70

57

19.72

7

Female

1.45

41

19.50

7

Male

1.52

37

16.01

7

Female

1.56

45

18.49

7

Male

1.41

31

15.59

7

Female

1.52

43

18.61

7

Male

1.43

41

20.05

7

Female

1.48

47

21.46

7

Male

1.49

67

30.18

7

Male

1.74

70

23.12

Year

Gender

Height (m)

Weight (kg)

BMI kg/m2

Year

Gender

Height (m)

Weight (kg)

BMI kg/m2

9

Male

1.85

55

16.07

9

Female

1.71

42

14.36

9

Male

1.54

48

20.24

9

Female

1.64

70

26.03

9

Male

1.67

60

21.51

9

Female

1.52

45

19.48

9

Male

1.62

40

15.24

9

Female

1.45

49

23.31

9

Male

1.46

45

21.11

9

Female

1.65

49

18.00

9

Male

1.82

66

19.93

9

Female

1.35

51

27.98

9

Male

1.70

51

17.65

9

Female

1.58

50

20.03

9

Male

1.75

63

20.57

9

Female

1.5

65

28.89

9

Male

1.66

46

16.69

9

Female

1.50

45

20.00

9

Male

1.60

68

26.56

9

Female

1.65

48

17.63

9

Male

1.76

55

17.76

9

Female

1.53

58

24.78

9

Male

1.71

68

23.26

9

Female

1.8

57

17.59

9

Male

1.63

40

15.06

9

Female

1.52

48

20.78

9

Male

1.70

42

14.53

9

Female

1.62

49

18.67

9

Female

1.53

48

20.50

9

Female

1.51

48

21.05

...read more.

Conclusion

The results to my further line of enquiry of how body mass index changes for Males and Females show that in general boys BMI is higher than the girls, and that the older you get the bigger the gap between the averages of males and females gets.

So the answer to the hypothesis is, the body mass index between each year varies, in the averages and the range.  The BMI between each gender varies in averages and in ranges as well.

Summary

  • There is a positive correlation between height and weight this means the taller you are the more you weigh.  Also I have worked out an equation from which I can calculate an estimate of what you height should be based on your weight and vice versa.
  • Height is affected by age and gender.  The older you are the taller in general you are and males in general are taller than females.  Also 28% of the boys in the school are between 1.6m and 1.8m.  The male average height is more than 75% of the girl’s heights in my stratified random sample.
  • Body mass index does not vary much between each year but the spread of the results is different for each year.  Males BMI is bigger than females BMI in general.  

...read more.

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