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  • Level: GCSE
  • Subject: Maths
  • Word count: 2729

Relationship between height and weight

Extracts from this document...

Introduction

GCSE MATHS COURSEWORK

Aim: My aim in this coursework is to find out about the relationship                                           between the height and weight. I will also find out if the Boys weigh more and are taller than the girls and vice versa. I will also find out what is the best category for height and weight that everyone will fit in. I will also find the mean median and range for all of them.

Hypothesis: My hypothesis is that the more taller you are the more you weigh, also that the girls will probably weigh more because I don’t think they will do as much exercise as the boys do, but I also know that the girls will be taller because scientists say that girls are taller than boys when they are younger. I would like to find out if that is true.

Method: I will take a random sample of boys and girls, I will do this by using the calculator using the buttons: SHIFT + RAND# =

Data representation: I will represent my data in many forms such as: Scatter graph, Pie charts, histograms, cumulative frequency, graph bar charts, table, etc.

No.

Gender

Height (m)

Weight (kg)

 1

M

1.63

60

2

M

1.75

45

3

F

1.83

60

4

F

1.67

52

5

M

1.8

49

6

M

1.66

70

7

M

1.9

70

8

F

1.6

54

9

F

1.52

45

10

F

1.62

56

11

F

1.55

36

12

F

1.8

60

13

F

1.67

66

14

M

1.67

66

15

M

1.7

57

16

F

1.6

56

17

M

1.71

57

18

M

1.52

60

19

M

1.66

66

20

M

1.6

59

21

F

1.63

44

22

F

1.63

44

23

F

1.4

45

24

F

1.73

51

25

M

1.8

60

26

F

1.72

51

27

M

1.72

63

28

M

1.75

56

29

M

1.91

82

30

M

1.77

57

31

F

1.68

54

32

F

1.73

64

33

F

1.73

50

34

F

1.63

47

35

F

1.72

56

36

F

1.62

48

37

F

1.56

50

38

M

1.8

60

39

M

1.55

64

40

F

1.75

57

41

M

1.63

50

42

M

1.86

56

43

F

1.73

51

44

M

1.81

72

45

M

1.75

60

46

M

1.72

58

47

F

1.62

48

48

M

1.54

57

49

M

1.54

66

50

F

1.69

51

This is showing the data set.

I will choose a random set of 10 boys and 10 girls, to do this I can do it in different ways such as in the calculator press SHIFT + RAND# =, or I can do it another way by writing every pupil number in the hat and randomly placing my hand and choosing 10 boys and 10 girls

I had chosen the calculator version.


MODE, MEAN, RANGE

I will first find the mean median and range for height and weight; I will do this because I want to see the best fit that average people should be in.

I will find the average by creating a frequency table:

Weight

Frequency

36-40

1

41-45

3

46-50

1

51-55

2

56-60

8

61-65

1

66-70

4

Now that I have done this, I will now create a pie chart to help me find the mode.

image00.png

As you can see by the pie chart, the mode is 56-60 so the average people should be/are between 50-60 kg.

I will now find the mean mode and range for weight:

To do this I will create another frequency table.

Weight

Frequency

Midpoint(x)

FxX

36-40

1

36+40÷2=38

1×38=38

41-45

3

41+45÷2=43

3×43=129

46-50

1

46+50÷2=48

1×48=48

51-55

2

51+55÷2=53

2×53=106

56-60

8

56+60÷2=58

8×58=464

61-65

1

61+65÷2=63

1×63=63

66-70

4

66+70÷2=68

4×68=272

Total=20

Total=1,120

...read more.

Middle

4

1.66-1.75

8

1.76-.185

2

1.86-1.95

1

Now I will create my pie chart. I will create a pie chart so that I can show the information that I have written in the Frequency table.

image01.png

As you can see by the pie chart, the mode is 1.66-1.75 so the average people should be is between 1.66-1.75 m.

I will now find the mean mode and range for Height:                              

To do this I will create another frequency table.

Height

Frequency

Midpoint(x)

FxX

1.45-1.55

3

1.5

4.5

1.56-1.65

5

1.605

8.025

1.66-1.75

8

1.705

13.64

1.76-1.85

3

1.805

5.415

1.86-1.95

1

1.905

1.905

Total=20

Total=33.485

Mean= to find it as a formula = FXX÷F

Mean=33.485÷20

Mean=1.67425 or 1.6 as normal round up.

I have now worked out my mean. I worked it out by finding my midpoint; I found my midpoint by adding up the ranges and divided it by 2, I then multiplied my midpoint to my frequency. I added all the totals up and divided it by the frequency total.

 I will now find my mode:

Mode= the range with the highest frequency.

Mode= 1.66-1.75

I have worked out my mode, now I will find out my range.

Range= the highest value takeaway the lowest.

Range= 1.9-1.52

Range= 0.38

I now know the mean mode and range for height.

I will now create a cumulative frequency graph for both height and weight.

Cumulative Frequency graphs

I will now create a tally for my cumulative frequency graph.

Height

Frequency

C.F

1.45-1.55

3

3

1.56-1.65

5

8

1.66-1.75

8

16

1.76-.185

3

19

1.86-1.95

1

20

I find out by C.F by adding the first frequency to the next, until I reach the end this will give me my cumulative frequency.

I have now completed my tally chart for my cumulative frequency. I found out my cumulative frequency by adding up the previous frequency.

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile. The reason why I am creating a cumulative frequency graph is so that I can work out my upper quartile, median, lower quartile and inter quartile

image10.png

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Inter Quartile=

.

I will now do the same for Weight:

Weight

Frequency

C.F

36-40

1

1

41-45

3

4

46-50

1

5

51-55

2

7

56-60

8

15

61-65

1

16

66-70

4

20

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile.

image11.png

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Inter Quartile=

Histogram:

I am going to create tally charts to help me find the frequency density

Weight

Frequency

F.D

36-40

1

0.25

41-45

3

0.75

46-50

1

0.25

51-55

2

0.5

56-60

8

2

61-65

1

0.25

66-70

4

1

I have found the frequency densities; I will create a histogram to compare later on.

image12.png

I will now do the same for height:

Height

Frequency

C.F

1.45-1.55

3

30

1.56-1.65

5

55.555

1.66-1.75

8

88.888

1.76-.185

3

33.333

1.86-1.95

1

11.111

I will now create a histogram for the height. I will do a histogram so that the information shown is more clearly.

image13.png

Now I will create a scatter graph for both height and weight, I want to do this because I want to see the line of best fit, this is were the students should really be at.

Scatter Graph:

To be able to create a scatter graph I will need to make frequency table:

Height (m)

Weight (kg)

 1.63

60

m

1.75

45

m

1.83

60

f

1.67

52

f

1.8

49

m

1.66

70

m

1.9

70

m

1.6

54

f

1.52

45

f

1.62

56

f

1.55

36

f

1.8

60

f

1.67

61

f

1.67

66

m

1.7

57

m

1.6

56

f

1.71

57

m

1.52

60

m

1.66

66

m

1.63

44

f

I have now created the table, now I will plot this to a scatter graph:

image14.png

As you can see there is a high collerence, most people go above the line of best fit.

Difference between boys and girls:

In this section I will try to find the difference between boys and girls.

Who weighs more?

I will now try and find out who weighs more by creating a pie charts, histogram and line graph.

To do this I will need to create a frequency table if I want create line graph.

Weight

Boys frequency

Girls frequency

36-40

0

1

41-45

1

2

46-50

1

0

51-55

0

2

56-60

4

4

61-65

0

1

66-70

4

0

...read more.

Conclusion

1

2

1.86-1.95

1

0

Now that I have done this, I will plot these in a histogram:

image07.png

Now I will make a Cumulative frequency graph for boys and girls Height:

Boys, first I will create the boys one and to do this I need to create a cumulative frequency table:

Height

Boys frequency

C.F

1.45-1.55

1

1

1.56-1.65

1

2

1.66-1.75

6

8

1.76-.185

1

9

1.86-1.95

1

10

Now I will plot this to a cumulative frequency graph:

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile.

image08.png

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Now I will create one for girls, to-do this I will need to create another frequency table:

Height

Girls frequency

C.F

1.45-1.55

2

2

1.56-1.65

4

6

1.66-1.75

2

8

1.76-.185

2

10

1.86-1.95

0

10

.

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile

image09.png

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

My final conclusion for the difference between girls and boys Height is that:

My hypothesis is wrong and that I never expected the boys to actually be taller.

...read more.

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