# Mayfield Coursework

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Introduction

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## Maths Coursework/Mayfield High School

In my Mayfield High coursework I am going to do three hypotheses. The first one is about the correlation between height and weight. I believe that the taller the person is, the heavier he is. My second hypothesis is a prediction to show that an older person is taller than younger people. Finally my third hypothesis will show that on average boys are taller than girls.

My hypotheses are:

- A = There is a positive correlation between height and weight.
- B = On average the students’ heights will become greater as they age.
- C = On average boys are taller than girls.

### Data

For both hypotheses I am going to use the Mayfield high school data. This specific data is secondary data as I have not personally taken it myself, another source ahs done it instead. It consists of the following:

- Year Group
- Surname
- Forename
- Age (Years and months)
- Gender
- Hair colour
- Eye colour
- Left/right handed
- Favourites (colour, type of music, subject, TV programme)
- Average number of hours TV watched per week
- IQ
- Height (m)
- Weight (kg)
- Distance between home and School
- Means of travel to school
- No. of siblings
- No. of pets
- KS2 results (Maths, English, Science)

I am going to get rid of all the unnecessary data, such as IQ and Favourite colour, as they are useless in my work. To take a sample from the data I am going to use STRATIFIED sampling. I will RANDOMLY take 20% from the boys from each year group and another 20% from the girls from each year group. This is so I can get the least bias and most accurate sample. This is so the result will be more accurate and be as fair as possible. If I just used a quota sample, where the population is divided into groups (gender, age, sex etc) and given number (quota)

Middle

10

106

94

21

19

11

84

86

17

17

Total

604

579

121

116

I worked out the sample by first finding out how many boys and how many girls there were in each year group. I then used the formula, =name of box*0.2, in each of the boxes in the “Amount of Sample” area. I had to round the amount of sample, as I cannot have a half of a person.

On each scatter diagram below it shows the equation to make the product moment correlation coefficient. For me to produce the actual result of the product moment correlation coefficient I would need to square root “R2”. The diagrams also show the correlation between the two sets of data, making it possible to compare them.

These are all my samples:

### Year 7 Girls

### Year 8 Girls

### Year 9 Girls

### Year 10 Girls

### Year 11 Girls

### Year 7 Boys

### Year 8 Boys

### Year 9 Boys

### Year 10 Boys

### Year 11 Boys

### Hypothesis 1

(There is a positive correlation between height and weight)

I believed that there is a positive correlation between height and weight. As you can see that on all of the graphs there is a positive correlation with a few of them (Yr 7 and 11 Boys) being a strong positive correlation.

The correlations between the height and weight are fairly strong. You can see this as the line of best fit is positive. This means that as the height of one person increases, their weight also increases; varying on the amount they grow.

A good example is of the Yr 11 boys’ graph. It shows that as the height increases, so does the weight.

This is an example from the Yr 11 boys’ graph; it shows that the person who is 1.78m, which is the smallest, tall weighs 37kg, which is also the smallest and the person who is 2.03m, which is the biggest, weighs 86kg, which is the biggest.

This clearly shows that there is a positive and fairly strong correlation between height and weight.

Height (m) | Weight (kg) |

1.78 | 37 |

1.82 | 66 |

1.85 | 73 |

2.03 | 86 |

Year | Gender | Spearman’s rank Correlation Coefficient |

7 | Boys | 0.664 |

Girls | 0.296 | |

8 | Boys | 0.149 |

Girls | 0.136 | |

9 | Boys | 0.148 |

Girls | 0.173 | |

10 | Boys | 0.170 |

Girls | 0.275 | |

11 | Boys | 0.707 |

Girls | 0.329 |

The above table shows the Spearman’s Rank Correlation Coefficient for each year and it is split into both of the genders. This is worked out by using the Product Moment Correlation Coefficient (on the top left hand corner of each graph) and square rooting it and rounding it to 3 decimal places. From the table you can see that the lowest figure is 0.136 and the highest is 0.707, which is a big difference in terms of Spearman’s Rank Correlation Coefficient. A very weak negative correlation would be -1, a balanced normal correlation would be 0 and a very strong positive correlation would be 1. 2 of the graphs have a fairly strong positive correlation, Yr 7 boys and Yr 11 girls. The rest of the figures have a weak positive correlation.

### Hypothesis 2

(On average the students’ heights will become greater as they age)

I will prove that on average the students’ heights will increase. Below are the graphs for boys and girls that show a correlation between year 7 and 9 and year 9 and 11. This will show that the height does increase as the students’ age. For the samples I will obtain them from both genders.

The above diagram is of two box and whisker diagrams from Yr 7 heights and Yr 9 heights. From this you can see that on average, the Yr 9 heights are greater than the Yr 7s, indicating that their age has increased through the two years. I have used box and whisker diagrams to make it easier to compare both sets of data.

The two histograms above are from the two sets of data, Yr 7s heights and Yr 9 heights. From this you can also clearly see that the Yr 9s median height is greater than the yr 7s. The Yr 9s also have a smaller percentage for the lower quartile.

Yr 7 Stats | Yr 9 Stats | |

Lower Quartile | 1.45 | 1.54 |

Upper Quartile | 1.62 | 1.66 |

Median | 1.54 | 1.58 |

Standard Deviation | 0.112095 | 0.0780745 |

Conclusion

### Evaluation

Overall, I think I have given accurate and reliable results for my investigation. I have taken out the outliers, used graphs to examine every hypothesis, and accurately calculated other figures like standard deviation and the mean. This helped me to identify correlations between the different data types and to provide me with reliable conclusions.

To improve my investigation, I would have used more factors from the Mayfield data, such as more pupils or from other schools. This would have given me more accurate results, because there would be more information to look at. Apart from that it would have been easier to identify any patterns and if I had more data to analyse I would have provided with more precise results

Apart from that I could have further developed my investigation by adding more hypotheses to examine other factors.

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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