# Height and Weight of Pupils

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Introduction

AO4 Coursework

Mayfield High School

HATCH END HIGH SCHOOL

Mathematics GCSE

Name: Daniel Desai

Candidate number: 4073

Tutor Group: 10/18

Teacher: Mr J Quaye

Date: 10/10/06

Planning

Introduction

In this project I will be investigating the heights and weights of pupils at Mayfield High School. Mayfield High School is not a real school, it is imaginary, and it has 1183 students altogether.

The distributions of the pupils in every year are below:

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 |

The data I will be working with is from the Edexcel Internet Database and it is secondary data. Every student has received this data. The data is of the fictitious school called Mayfield High School. The data they have given for each pupil is their Name, Year group, IQ, Weight, Height, Hair colour, Eye colour, Distance from home to school, Usual method of travel to school, Number of brothers or sisters, Key stage 2 results in English, Mathematics and Science.

I have preferred to use secondary data rather than primary data because it is more suitable; primary would take a very long time but it would be a higher degree of accuracy. The advantages of secondary data is it is easy to find and due to the short amount of time provided to complete this coursework it will be more suitable.

I will not be using qualitive data I will be using quantitve data.

Middle

David

Male

100

1.60

50

10

Chung

Jason

Male

109

1.71

56

10

Koonen

jung

Male

91

1.75

45

10

Leahy

Cliff

Male

103

1.65

54

10

Leech

Alistair

Male

102

1.65

55

10

Petit

Neil

Male

107

1.80

54

10

Tumasi

Rolo

Male

102

1.50

65

10

Ashiq

Azra

Female

95

1.60

56

10

Bhatti

Sadia

Female

94

1.62

48

10

Campbell

Debbie

Female

96

1.55

55

10

Johnston

Summer

Female

105

1.50

40

10

Khaliq

Nazia

Female

93

1.62

48

10

Razwana

Tahira

Female

90

1.62

46

10

Taylor-Wall

Angela

Female

106

1.70

55

10

Thorpe

Katrina

Female

95

1.57

54

11

Askabat

Fernado

Male

105

1.71

57

11

Ballson

James

Male

101

1.52

60

11

Cripp

Justin

Male

100

1.67

50

11

Friend

Aaron Carl

Male

102

1.73

60

11

Hussain

Muhammad

Male

90

1.82

52

11

Kage

Jai

Male

118

1.5

35

11

Khan

Assad

Male

100

1.68

63

11

Ableson

Anbigale

Female

98

1.83

60

11

Ali

Amera

Female

90

1.62

56

11

Chen

Sabrina

Female

117

1.61

54

11

Compass

Sharon

Female

106

1.52

38

11

Durst

Francesca

Female

95

1.75

60

11

Heap

Louise

Female

92

1.80

42

11

Kavangh

Jonna

Female

100

1.60

48

I will investigate these following hypotheses using my sample of data:

Hypotheses

- Year 8 females will be taller and heavier than year 8 males.
- Year 11 males will be taller and heavier than year 11 females.
- Year 8 males will be taller and heavier than Year 7 males but shorter and lighter than Year 11 males.
- There is a positive correlation between height and weight.

I have chosen these hypotheses according to my experiences, general knowledge and what I have seen. Scientific research shows females reach maturity earlier than males. Also females usually have a greater weight and height during the years 12-14. Males reach maturity between the ages of 14-16 and Year 11 males have already matured and have started their growth spurts. Due to this development the height to weight ratio is greater in Years 7 and 8 for females rather than males. But Years 9-11 males have a greater height to weight ratio than the females.

To prove that my hypotheses are correct I will draw these diagrams:

- Histogram- my data is continuous and will be grouped. The shape will affect the measure of average and dispersion to be used. The mode can be estimated from this diagram.
- Cumulative frequency curve- for the height and weight will change the cumulative frequency as the data greatens. I will be using box and whisker plots to make in parallel to make it easier. I will be using the skewness.
- Scatter graph- to show the connection between the heights and weights across the gender divide so to show the quality of the correlation. I will use different graphs for male and female. The scatter graph can help me make estimates about height and weight by using the line of best fit.

I will calculate the mean, median, mode, interquartile range and standard deviation to find differences and similarities between the years. I will use this data to estimate the height to weight ratio. The standard deviation will show the dispersion.

From my random sampling I had a few outliers. They were:

Year Group | Surname | Forename | Gender | IQ | Height (m) | Weight (kg) |

7 | Ahmoud | Asif | Male | 101 | 1.42 | 26 |

7 | Bolton | Paul | Male | 106 | 1.65 | 69 |

8 | Christopher | Steven | Male | 100 | 1.35 | 29 |

8 | Rashid | Azrah | Female | 103 | 1.58 | 72 |

9 | Miya | Gallahad | Male | 96 | 1.82 | 75 |

10 | Air | Jason | Male | 116 | 1.90 | 70 |

11 | Kage | Jai | Male | 118 | 1.5 | 35 |

Conclusion

This shows that my hypothesis is correct.

Percentage Error

To calculate the percentage error the formula is Cumulative median . This is

Raw data median

how I shall calculate the percentage error. I shall only work it out for the years that I have done which are Yrs 7, 8 and 11.

Yr 7 Males Height

Cumulative median = 1.541m

Raw data median = (13+1) = 1.52m

2

Percentage error = 1.013815789

Yr 7 Females Height

Cumulative median = 1.55m

Raw data median = (11+1) = 1.52m

2

Percentage Error = 1.019736842

Yr 7 Males Weight

Cumulative median = 43kg

Raw data median = (13+1) = 40kg

2

Percentage Error = 1.075

Yr 7 Females Weight

Cumulative median = 41.6kg

Raw data median = (11+1) = 40kg

2

Percentage Error = 1.04

Yr 8 Males Height

Cumulative median = 1.545m

Raw data median = (12+1) = 1.6m

2

Percentage Error = 0.965625

Yr 8 Females Height

Cumulative median = 1.575m

Raw data median = (11+1) = 1.58m

2

Percentage Error = 0.996835443

Yr 8 Males Weight

Cumulative median = 43.9kg

Raw data median = (12+1) = 50kg

2

Percentage Error = 0.878

Yr 8 Females Weight

Cumulative median = 50.6kg

Raw data median = (11+1) = 50kg

2

Percentage Error = 1.0

Yr 11 Males Height

Cumulative median = 1.685m

Raw data median = (7+1) = 1.68m

2

Percentage Error = 1.00297619

Yr 11 Females Height

Cumulative median = 1.64m

Raw data median = (7+1) = 1.62m

2

Percentage Error = 1.012345679

Yr 11 Males Weight

Cumulative median = 57kg

Raw data median = (7+1) = 57kg

2

Percentage Error = 1.0

Yr 11 Females Weight

Cumulative median = 54.8kg

Raw data median = (7+1) = 54kg

2

Percentage Error = 1.004814815

Standard Deviation

I will do standard deviation for all the males, females and then every student. The standard deviation will show the dispersion. The formula for standard deviation is:

Σ (x –m) 2 Σ = Sum of

x = Height/Weight all added up

Σ F m = mean

2 = squared

F = frequency

Males Height

Frequency = 51

Mean = 50.8627451

Sum of (mean – height) squared =

Standard Deviation =

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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## Here's what a teacher thought of this essay

There are one or two good ideas in this work but there are too many missing diagrams to make it a good piece of work. 2 stars

Marked by teacher Mick Macve 18/03/2012