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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.

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 1.6 56 10 Connerly Jenny 15 10 September Female 1.7 48 10 Gorst Francesca 15 5 February Female 1.6 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 1.6 66 11 Turner Louise 16 8 November Female 1.6 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 1.5 43 7 Andrew Sohail 11 11 August Male 1.5 41 7 Thomson Damien 12 5 February Male 1.5 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 1.6 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 1.5 52 7 Pham Julie 12 1 June Female 1.5 40 7 Carney Esther 12 1 June Female 1.5 44 7 Marton Jan 12 6 January Female 1.5 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 1.6 57 7 Minton Jennifer 11 11 August Female 1.6 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

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.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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