# There is a weak positive correlation between height and weight for both girls and boys at Mayfield High School.

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Introduction

Maths Coursework

For my coursework, I will need to collect and use data on a number of students. I can obtain this data from a database provided by the exam board about Mayfield High School students. This is a fictitious school but the data is based on a real school, therefore the data that I will use from the database is reliable and will therefore let me draw conclusions accurately.

The database contains information about 1183 students. As this would be very difficult to use and analyse, I will be sampling from the total number to provided much smaller yet accurate information for me to work with.

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Hypotheses

1. There is a weak positive correlation between height and weight for both girls and boys at Mayfield High School.

I will begin to assess this first hypothesis by first taking a small fraction of the total number of pupils in the school, in order to investigate the relationship between height and weight at Mayfield High School.

I will take a stratified sample of 47 pupils, as 4% of the total number of 1183 is 47.32. This should give me a suitable number to sample and work with as it isn’t too large or too small, as to not deliver an accurate reading.

This is achieved, by taking the total number of pupils, either boys or girls, and dividing it by the total number of pupils through out the whole school, and then multiplying this by the total number that you want sampled.

To decide which pupils will be selected from each year groups, a random number generator will be used to make the method of selection unbiased and allowing every pupil the same chance of being selected. This can be done on either a calculator or in Microsoft excel.

Middle

Teyuba Dalton

1.62

80

Year 9 Boys

They were numbered from 1 to 118.

Sample Number | Random No | Name of Pupil | Height (m) | Weight (kg) |

1 | 56 | Asim Humza | 1.70 | 42 |

2 | 95 | Geoff Rowley | 1.56 | 53 |

3 | 72 | Thomas Killingham | 1.60 | 49 |

4 | 104 | David Smith | 1.70 | 48 |

5 | 39 | Edward Glenn | 1.48 | 40 |

Year 9 Girls

They were numbered from 1 to 143.

Sample Number | Random No | Name of Pupil | Height (m) | Weight (kg) |

1 | 23 | Chantelle Brown | 1.8 | 62 |

2 | 100 | Louise O’Donald | 1.55 | 36 |

3 | 13 | Laura Bertwistle | 1.48 | 47 |

4 | 105 | Ruth Peacock | 1.53 | 57 |

5 | 17 | Suki Bosh | 1.52 | 52 |

6 | 82 | Rebekah Langtle | 1.51 | 65 |

Year 10 Boys

They were numbered from 1 to 104.

Sample Number | Random No | Name of Pupil | Height (m) | Weight (kg) |

1 | 64 | Kuta Lister | 1.62 | 72 |

2 | 85 | Shida Saj | 1.65 | 68 |

3 | 19 | Stephen Browning | 1.77 | 57 |

4 | 24 | Jason Chung | 1.71 | 56 |

Year 10 Girls

They were numbered from 1 to 94.

Sample Number | Random No | Name of Pupil | Height (m) | Weight (kg) |

1 | 32 | Serena Fox | 1.90 | 40 |

2 | 16 | Emily Brown | 1.62 | 54 |

3 | 23 | Jenny Connerly | 1.70 | 48 |

4 | 64 | Nichole Morrison | 1.63 | 48 |

Year 11 Boys

They were numbered from 1 to 84.

Sample Number | Random No. | Name of Pupil | Height (m) | Weight (kg) |

1 | 73 | Russell Simmons | 1.65 | 50 |

2 | 17 | Peter Cullen | 1.88 | 75 |

3 | 63 | Ahmed Nolan | 1.84 | 78 |

Year 11 Girls

They were numbered from 1 to 84.

Sample Number | Random No. | Name of Pupil | Height (m) | Weight (kg) |

1 | 32 | Davina Grace | 1.65 | 54 |

2 | 8 | Heidi Becher | 1.72 | 51 |

3 | 55 | Billie McCreadie | 1.63 | 38 |

Having taken all of my samples, from the students, I took all of the heights and weights of the boys and all of the heights and weights of the girls, and plotted them on a scatter graph, to see whether there was a weak positive correlation between the boys and girls.

I did this by taking the heights and weights of the boys and girls from the tables above and sorting them into two columns for by gender.

Next I highlighted all of the data and went to the table wizard. Here I chose the XY Scatter Graph option and in the ‘Series’ menu chose to distinguish the data of the girls from the boys. As they already had all the information about the boys in ‘Series 1,’ I added another Series and labelled it ‘Girls’.

Conclusion

Graph showing the height of girls and boys from year 7 and year 11

The graph above shows that the boys do in fact have a greater growth spurt than girls. This is shown as the area between the lines showing the heights of the boys are greater than those of the girls.

Conclusion

Overall, having drawn interpretations for each hypothesis individually, I think that in some categories there was a trend as you went up the school. For example, the line graph for my fourth hypothesis shows that as the boys got older their weights increased steadily with their age, with only a few exceptions.

I also noticed this trend with the graph I drew with in hypothesis five. Both boys and girls’ heights increased steadily with age, with only a few outliers who did not grow that much.

However these results could have been affected by the size of the sample. The samples were only a small representative value for each year group. Unseen anomalies could have occurred through people with conditions that I may not have picked up. My data may not have been totally accurate, as I may have selected the same people many times for my sampling.

Also with some of my results, I noticed that as the students got older, they seemed to all be in the same height and weight categories. This is shown particularly in the hypothesis I did on Body Mass Index. The outlying class widths seemed to disappear and move towards the main class widths in the centre. This effect was also shown in the box plots that I plotted. The difference between the ranges decreased dramatically with age.

I believe I did this coursework quite accurately as I did take into account and compensate for most anomalies, and other outliers in the database. Although, I may not have taken a sufficient number of people to sample, or have taken into account anomalies that could have gone unnoticed in the database.

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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