Conduct an investigation comparing height and weight from pupils in Mayfield School.

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Noel Modarres Mathematics Coursework

In this investigation, I have been given data from Mayfield School. Although the name of the school is likely to be fictional the data itself has come from real students. The data I have been given is for year 7 and year 11 students. There is information on around 170 students for each year. The following are the types of information we got on each student, year group, surname, forename, age, gender, hair colour, eye colour, which handed they are, favourite colour, favourite music, favourite sport, favourite subject, favourite T.V programme, average hours of T.V watched, IQ, height (m), weight (kg), distance travelled to school, Means of transport to school, number of siblings, number of pets, key stage two results for, maths, English and science.

From the data I have received I have chosen to conduct an investigation comparing height and weight because I feel there much relevance between ones and height and weight. I have chosen to compare height and weight because I feel I will get clear results and therefore conduct a meaningful and knowledgeable investigation. I will be trying to determine whether ones height has any relevance to ones weight and then I will attempt to find out whether separating boys from girls will show different trends and in general have much difference from the group as a whole.

I will first investigate heights and weight for year 7 and for year 11 and as an extension I will make comparisons and comment for both years. For my investigation I will need to start with a random sample of 50 students (25 girls, 25 boys) from year 7. I have data from a total of around 170 students, and the amount of boys and girls are roughly even, hence meaning there are about 85 boys and 85 girls. To get a completely unbiased sample of students I will be using random selection. I have figured out that because there are around 85 boys it will be sensible to choose every third boy in the list starting with the third boy down the list. Theoretically this will mean that around 10 students will not even be considered at the bottom of the list because 3 × 25 = 75 and 85 - 75 = 10. However this method of random selection will give me a completely random and unbiased sample of student. The exact same applies for the girls. When I have done the random sample selection I will have a total of 50 students, 25 of which are boys and 25 of which are girls.

I will now conduct a plan in the forms of a flow chart to show what I plan to do and the types of things I intend on finding out.

Plan

The students I selected from the sample. My random sample was gained by choosing every third boy and girls form the list.

Name

Height (cm)

Weight (kg)

Oliver Fred Afsal

55

53

Asif Ahmoud

42

26

Sohail Farooq Andrew

50

41

Wayne Paul Ashcroft

52

37

David Michael Barding

64

50

Mikeal Christophe Bodman

49

38

Rhys Boyo

47

41

Ben Brown

58

40

Avais Butt

60

50

Stephen Campble

52

32

Andrew Brown Chavies

59

52

Neil Cohen

55

38

Nick Michael Connaugto

62

48

Stephen Cronie

35

29

James Dean Davies

57

55

Ben Dever

65

52

James George

61

63

Thomas Green

54

38

Davison Hagrid

75

62

Rhys Hardy

51

45

Stephen Hog

40

40

Anthony Hughes

44

42

Aysham Jebron

59

47

Mark Anthony Jones

51

59

Mathew David Kennedy

48

47

Name

Height (cm)

Weight (kg)

Zahrah Anderson

56

53

Holly Dempsey Bates

61

47

Vicky Joanne Biddle

58

50

Kelly Brandwood

59

54

Nealy Leah Brown

63

50

Esther Carney

50

44

Claire Elizabeth Clarke

59

38

Rebecca Louise Collins

45

52

Clara Croft

58

48

Sarah Cullen

57

45

Elizabeth Dean

55

50

Sarah Ditchmoor

64

44

Maggie Dougan

49

53

Sioban Jane Ennis

56

57

Natasha Caralone Gate

32

40

Tanya Harding

53

40

Julie Harrison

30

36

Joanne Alicia Higgins

50

45

Karen Hughes

63

51

Melissa Ann Hunt

65

43

Julie Jade Jackson

41

40

Jessica Jane Jones

75

47

Danielle Kelly

47

44

Jessica Louise Kelly

20

38

Hira Khalid

19

47

Here is more useful representation of the data. Here are the frequency table for height and weight separated into boys and girls. The height and weight is continuous data.

Boys

Height, h (cm)

Tally

Freq.

10 ? h < 120

0

20 ? h < 130

0

30 ? h < 140

|

40 ? h < 150

|||| |

6

50 ? h < 160

|||| |||| ||

2

60 ? h < 170

||||

5

70 ? h < 180

|

Total

25

Weight, w (kg)

Tally

Freq.

25 ? w < 30

||

2

30 ? w < 35

|

35 ? w < 49

||||

4

40 ? w < 45

||||

5

45 ? w < 50

||||

4

50 ? w < 55

||||

5

55 ? w < 60

||

2

60 ? w < 65

||

2

Total

25

Girls

Height, h (cm)

Tally

Freq.

10 ? h < 120

|

20 ? h < 130

|

30 ? h < 140

||

2

40 ? h < 150

||||

4

50 ? h < 160

||||| ||||| |

1

60 ? h < 170

||||

5

70 ? h < 180

|

Total

25

Weight, w (kg)

Tally

Freq.

25 ? w < 30

0

30 ? w < 35

0

35 ? w < 40

|||

3

40 ? w< 45

||||| ||

7

45 ? w < 50

||||| |

6

50 ? w < 55

||||| |||

8

55 ? w < 60

|

60 ? w < 65

0

Total

25

To make comparisons between the sets of data I will put this in formation into frequency polygons. (Please refer to the frequency polygon on page 5).

I will now put the information from my frequency tables into stem and leaf diagrams so that I can find the mean, modal class interval (because it is continuous data), median and range for the height and weight for the boys and girls.

Key

Stem and leaf diagram for height 110 | 9 = 119

Stem

Leaf

Freq.

10

9

20

0

30

0,2

2

40

,5,7,9

4

50

0,0,5,5,6,6,7,8,8,9,9

1

60

,3,3,4,5

5

70

5

Total

25

Boys Girls

Stem

Leaf

Freq.

10

0

20

0

30

5

40

0,2,4,7,8,9

6

50

0,1,1,2,2,4,5,5,7,8,9,9

2

60

0,1,2,4,5

5

70

5

Total

25

Heights (cm)

Mean

Modal Class Interval

Median

Range

Boys

54

50 - 160

54

40

Girls

51

50 - 160

56

56

The mean height of the boys is higher than the mean height for the girls; the modal class interval is the same for both boys and girls. However the median for the girls is higher than the boys, also the range of the girls 0.56m is much more spread out compared to 0.4m for the boys. The evidence from the sample suggests that 13 out of 25 or 52% of boys have a height that is between 150 - 160cm, whereas 11 out of 25 or 44% of girls have a height between the same interval. The frequency polygon shows that more girls than boys have a height less than 140cm, but more boys than girls have a height more than 150cm. These results are based on a random sample of 25 boys and 25 girls. To confirm my results I could extend my sample or try a completely new sample and compare the results.

Key

Stem and leaf diagram for weight 25 | 1 = 26

Stem

Leaf

Freq.

25

0

30

0

35

,3,3

3

40

0,0,0,3,3,4,4,4

8

45

0,2,2,2,3

5

50

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

8

55

2

60

0

Total

25

Boys Girls

Stem

Leaf

Freq.

25

,4

2

30

2

35

2,3,3,3

4

40

0,0,1,1,2

5

45

0,2,2,3

4

50

0,0,2,2,3

5

55

0,4

2

60

2,3

2

Total

25

Weight (kg)

Mean

Modal Class Interval

Median

Range

Boys

43

40 - 45 and 50 - 55

45

37

Girls

46

40 - 45 and 50 - 55

47

21

The mean weight and median for the girls is higher than the mean and median weight for the boys. Boys and girls have both 40 - 50kg and 50 - 55kg as their modal class interval. The range for the boys 0.37 is much higher than the girls range 0.21. The evidence from the sample suggests 8 out of 25 or 32% of the girls have a height between 50 - 55kg. Also that 6 out of 25 or 24% of boys have a weight between 40 - 45kg. The evidence also suggest that 16% more boys than girls have a weight below 40kg. The frequency polygon shows that more girls than boys have a weight between 40 - 55kg. These results are based on a random sample of 25 boys and 25 girls, to confirm my results I could extend my sample or use another random sample and compare the results.

I will now make a hypothesis about my data and try to back it up with scatter graphs.

My hypothesis is that the taller you are the more you are likely to weigh.

(Please refer to the scatter graph on page 9)

As you can see there is positive correlation, however the correlation was not very strong indicating my hypothesis, the taller you are the more your likely to weigh was correct but not very accurate. The correlation being positive but not very strong indicates that it is likely that the taller you are, the more your likely to weigh, but not for all students. This is the general case, however there are a freak results such as the girl who weighs 47kg, but is only 119cm tall. This upsets the trend of the data. But generally the scatter diagram indicates that the taller you are the more you're likely to weigh. The line of best fit suggests someone that is 150cm tall is likely to weigh 43kg and someone who weighs 55kg is likely to be 166cm tall.

I now hypothesise that separating boys and girls will produce stronger correlation between height and weight. (Please refer to the scatter graphs on page 10).

The evidence supports my hypothesis that there will be stronger correlation between height and weight if boys and girls are considered separately. For boy the line of best fit suggests that boy who is 160cm tall will weigh 58kg and someone who weighs 40kg will be 148cm tall. For girls the line of best fit suggests that a girl who is 170cm tall will weigh 59kg and a girl who weighs 35kg will be 135 cm tall.

Equation of the lines

(Please refer to the graph on page 11)

Boys

Gradient = 1

Intercept = 128

y = mx + c

y = 1x + 128

x = y - 128

1

So if a boy is 140cm tall the equation of the line would suggest

If y = 140 then

x = 140 - 128 = 12 = 12 (12 + 25 = 37)

1 1

The first value on graph is 25, so 25 + 12 = 37kg

So the equation of my line of best fit for boys suggests that a boy who is 140cm tall will weigh 37kg.

Girls

Gradient = 1.6

Intercept = 113

y = mx + c

y = 1.6x + 113

x = y - 113

1.6

So if a girl is 161cm tall the equation of the line would suggest

If y = 161cm then

X = 161 - 113 = 48 = 30 (30 + 25 = 55)

1.6 1.6

The first value on my graph is 25, so 25 + 30 = 55

So the equation of my line of best for girls suggests that a girl who is 161cm tall will weigh 55kg.
Join now!


Mixed

Gradient = 1.3

Intercept = 123

y = mx + c

y = 1.3x + 123

x = y - 123

1.3

So if a person is 175cm tall the equation of the line would suggest

If y = 174cm then

X = 175 - 123 = 42 = 40 (40 + 25 = 65)

1.3 1.3

The first value on my graph is 25, so 25 + 40 = 65

So the equation of my line of best for girls suggests that a ...

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