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  • Level: GCSE
  • Subject: Maths
  • Word count: 3797

Boys are taller than girls, I am going to investigate this by looking at a stratified sample of boys and girls separately across years seven and eleven, and forming a cumulative frequency graph to compare the heights between them.

Extracts from this document...

Introduction

******* *****

11R2

Data Handling Coursework

Mayfield Highschool

Introduction

The coursework I’m about to do is based on the height of pupils at Mayfield Highschool.  I’m going to explore two hypotheses with secondary source data. My first hypothesis is that; boys are taller then girls, I am going to investigate this by looking at a stratified sample of boys and girls separately across years seven and eleven, and forming a cumulative frequency graph to compare the heights between them. My sample size is going to be 100. But before creating my sample I am going to remove any bias pieces of data that sets the rest of the population askew. I am then going to work out each strata size. The strata size is represented by proportion.

Example

Sample size 30

Year

Number of pupils

Sample size

Year 11

207

207/346x30=17.9 (18 pupils)

Year 12

81

81/346x30=7.02 (7 pupils)

Year 13

58

58/346x30=5.03 (5 pupils)

Total

346 pupils

30 pupils

Once I have created my samples I am going to use a random number generator ‘RNG’ to select the data I’m going to use. I’m going to use a ‘RNG’ so that is a fair selection process opposed to counting them out, i.e. every 3rd person will be used. This method isn’t fair as the people after my sample size won’t be used. I.e. my sample size is 18 numbers 54 onward won’t be used.

...read more.

Middle

February

Female

1.68

36

9

Green

Nichola

14

10

September

Female

1.36

38

9

Green

Sahara

14

2

May

Female

1.54

54

9

Guzman

Victoria

14

10

September

Female

1.75

65

9

Hulme

Louise

14

4

March

Female

1.62

58

9

James

Lucy

14

8

November

Female

1.71

40

9

Khan

Humspira

14

6

January

Female

1.69

48

9

Mosler

Samantha

14

2

May

Female

1.58

36

9

Williams

Ashley

14

9

September

Female

1.65

48

Year 10

10

Ashiq

Azra

15

0

July

Female

1.60

56

10

Connerly

Jenny

15

10

September

Female

1.70

48

10

Gorst

Francesca

15

5

February

Female

1.60

50

10

Hall

Lisa

15

2

May

Female

1.78

52

10

Hall

Faith

15

4

March

Female

1.55

48

10

Lawson

Karren

15

7

December

Female

1.75

50

10

Thorpe

Katrina

15

4

March

Female

1.57

54

10

Yo

Rhonda

15

7

December

Female

1.52

47

Year 11

11

Butt

Paveen

16

10

September

Female

1.65

54

11

Flawn

Elise

16

8

November

Female

1.62

51

11

Kay

Nadia

16

11

November

Female

1.62

42

11

Raphiell

Sally

16

3

April

Female

1.55

50

11

Skeely

Jenifer

16

7

December

Female

1.60

66

11

Turner

Louise

16

8

November

Female

1.60

55

11

Zarrent

Donna

15

11

August

Female

1.67

48

This is my cumulative frequency table

Boys

Height Group (m)

Tally

Frequency

Cumulative frequency

1.30≤x<1.35

0

0

1.35≤x<1.40

III

3

3

1.40≤x<1.45

III

3

6

1.45≤x<1.50

IIII

5

11

1.50≤x<1.55

IIII

IIII

9

20

1.55≤x<1.60

IIII

5

25

1.60≤x<1.65

IIII

5

30

1.65≤x<1.70

III

3

33

1.70≤x<1.75

IIII

5

38

1.75≤x<1.80

IIII

5

43

1.80≤x<1.85

IIII

5

48

1.85≤x<1.90

III

3

51

Girls

Height Group (m)

Tally

Frequency

Cumulative frequency

1.30≤x<1.35

0

0

1.35≤x<1.40

II

2

2

1.40≤x<1.45

I

1

3

1.45≤x<1.50

IIII

4

7

1.50≤x<1.55

IIII

I

6

13

1.55≤x<1.60

IIII

I

6

19

1.60≤x<1.65

IIII

IIII

IIII

14

33

1.65≤x<1.70

IIII

I

7

40

1.70≤x<1.75

IIII

5

45

1.75≤x<1.80

IIII

4

49

Cumulative Frequency Graph showing the hypothesis boys are taller then girls

Lower Quartile (LQ)

Median

Upper Quartile (UQ)

Boys

12.75

25.5

38.25

Girls

12.25

24.5

36.75


From my graph I noticed that boys are taller then girls at the top end of the graph and at the bottom end of the graph. I think this is because girls go through puberty before boys so they tend to have their growth spurts before boys. I now want to know when exactly the boys over take the girls in the height stakes. I am going to do this by exploring my second hypothesis: Boys are always taller than girls. I am going to explore this hypothesis by randomly selecting 15 boys and 15 girls out of each year and creating box plots for each year.

Yr 7 boys

7

Hughes

Anthony

12

2

May

Male

1.44

42

7

Madden

Ben

12

0

July

Male

1.47

47

7

Cullian

Sabor

12

8

December

Male

1.50

43

7

Andrew

Sohail

11

11

August

Male

1.50

41

7

Thomson

Damien

12

5

February

Male

1.50

55

7

Jones

Danny

12

5

February

Male

1.53

38

7

Winstanley

Paul

12

4

May

Male

1.53

45

7

Lillie

Ben

12

7

December

Male

1.54

51.5

7

Butt

Avais

12

7

December

Male

1.60

50

7

Marks

Jonathan

12

7

December

Male

1.61

46

7

James

Kaprica

12

5

February

Male

1.64

55

7

Seedat

Sajeed

12

8

November

Male

1.65

46

7

Mamood

Asim

12

10

September

Male

1.67

60

7

Spencer

Joshua

12

7

January

Male

1.72

75

7

Hagrid

Davison

12

10

September

Male

1.75

62

Yr 7 girls

7

Wou

Chow Ting

11

11

August

Female

1.42

30

7

Davies

Louise

11

11

August

Female

1.48

46

7

Marton

Jan

12

6

January

Female

1.50

52

7

Pham

Julie

12

1

June

Female

1.50

40

7

Carney

Esther

12

1

June

Female

1.50

44

7

Marton

Jan

12

6

January

Female

1.50

52

7

Pham

Phuong

12

2

May

Female

1.51

41

7

Dodman

Emma

12

1

May

Female

1.53

52

7

Lewis - Goff

Kirsty

12

7

October

Female

1.53

57

7

Hall

Sarah

12

2

May

Female

1.58

45

7

Vickers

Holly

12

9

September

Female

1.60

57

7

Minton

Jennifer

11

11

August

Female

1.60

50

7

Burton

Emily

12

10

September

Female

1.61

48

7

Benjamin

Emma

12

8

November

Female

1.63

45

7

Kelly

Jessica

12

9

October

Female

1.66

45



Yr 8 boys

8

Asheq

Amir

13

7

December

Male

1.42

26

8

Roberts

Michael

13

3

April

Male

1.48

40

8

Mince

Shane

13

1

June

Male

1.50

39

8

Boye

Jay

13

4

March

Male

1.52

60

8

Kevill

Dean

13

2

May

Male

1.52

43

8

Smith

Ben

13

2

May

Male

1.55

74

8

Seattle

Waieed

13

4

March

Male

1.57

50

8

Phil

Faheem

13

4

April

Male

1.57

51

8

Thornley

John

13

4

April

Male

1.57

62

8

Wood

Andrew

13

1

June

Male

1.60

38

8

Ahaz

Asif

...read more.

Conclusion

1.60

54

10

Bolton

Margarette

15

3

April

Female

1.62

48

10

Morrison

Nichole

15

10

September

Female

1.63

48

10

McVey

Joanne

15

6

January

Female

1.65

60

10

Tahir

Yasin

14

11

August

Female

1.67

48

10

Fawn

Attoosa

15

10

September

Female

1.73

45

10

Long

Anne

15

3

April

Female

1.74

47

10

Durst

Freda

15

4

March

Female

1.75

60

10

Dickson

Amy

15

9

October

Female

1.75

56

Yr 11 boys

11

Francis

Henry

16

7

January

Male

1.58

54

11

Cripp

Justin

16

6

September

Male

1.67

50

11

Lewis

James

16

11

September

Male

1.68

56

11

Askabat

Fernado

16

2

June

Male

1.71

57

11

Browne

William

16

1

June

Male

1.72

58

11

Fisher

Chis

16

5

February

Male

1.8

72

11

Major

William

16

0

July

Male

1.8

68

11

Biggleoskess

Frederick

16

2

May

Male

1.8

60

11

Hussain

Muhammad

16

4

March

Male

1.82

52

11

Lee

Brett

16

2

May

Male

1.83

75

11

Warne

Michael

16

3

April

Male

1.84

76

11

Frost

James

16

2

May

Male

1.85

73

11

Nadeem

Ammad

16

7

December

Male

1.97

84

11

Nadeem

Ammad

16

7

December

Male

1.97

84

11

Hossany

Selim

16

5

February

Male

2

86

Yr 11 girls

11

Green

Teresa

16

2

September

Female

1.37

30

11

Raphiell

Sally

16

3

April

Female

1.55

50

11

Biddle

Vicky

16

0

July

Female

1.56

50

11

McMillan

Collen

16

7

October

Female

1.58

48

11

Kay

Nadia

16

11

November

Female

1.62

42

11

Brown

Amy

16

2

May

Female

1.62

54

11

McCreadie

Jenny

16

10

September

Female

1.62

38

11

Butt

Paveen

16

10

September

Female

1.65

54

11

Ratty

Louise

15

11

August

Female

1.65

59

11

Acton

Jenny

16

3

November

Female

1.67

52

11

Jackson

Debi

16

1

June

Female

1.68

50

11

Warwick

Emma

16

8

November

Female

1.69

50

11

Feehily

Christina

16

6

January

Female

1.72

60

11

Mitchell

Nikayah

16

10

September

Female

1.73

48

11

Jonson

Kirten

16

8

September

Female

1.74

39

Conclusion

After studying the box plots alongside the cumulative frequency graph I noticed the box plots and the graph, display similar data. I noticed that the boys always have more variation in height. I think this is because in puberty there is a wide variation in boys of when they start they’re final growth spurt. I think if I carried this study on into tertiary education the boys range of height would even out with the girls and eventually be taller then them. Within my survey boys are taller then girls at the start and end of secondary school. This indicates that girls start puberty before boys in the middle years of secondary school, I looked at the box plots to indicate exactly when and it is in year 8 that girls start puberty. Also from my survey I evidently got my answers to my hypothesis. I found out boys are NOT always taller then girls but it is true that boys are taller then girls in general.

...read more.

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