# Mayfield Coursework

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Introduction

Maths Coursework

I have been given the task to test various hypotheses through using statistical information of a fictional school called Mayfield High. I have been given various pieces of information about this school but I will first need to extract the useful information which can help me to test these hypotheses.

Firstly, here is the hypothesis’s I have decided on:

1. Boys will be taller on average than girls

2. Boys will on average weigh more than what girls do.

3. As the age of a boy increases so does his weight.

4. The taller someone is the heavier they will be.

Before I test these hypotheses, I must first gain the useful data which will help me test them. Since the amount of students in each gender of every year varies, I must use a stratified sample. This means that I will use an equal percentage of each gender in every year throughout the school, making the sampling fair.

I want to have a sample of about 120 students. This is because the data I will gain from these 120 students will be highly useful and not too confusing for me to handle. There are 1183 students in the whole school and 120 is about 10%, which seems to be quite a good percentage to use.

To work out the number of pupils I would use in my hypothesis in each gender of every year group I will use the the following method:

Middle

150 ≤ w < 155

3

5

155 ≤ w < 160

2

7

160 ≤ w < 165

1

8

165 ≤ w < 170

4

12

170 ≤ w < 175

2

14

175 ≤ w < 180

0

14

180 ≤ w < 185

1

15

Height (cm)

Frequency

Cumulative Frequency

120 ≤ w < 125

0

0

125 ≤ w < 130

1

1

130 ≤ w < 135

0

1

135 ≤ w < 140

0

1

140 ≤ w < 145

2

3

145 ≤ w < 150

0

3

150 ≤ w < 155

2

5

155 ≤ w < 160

1

6

160 ≤ w < 165

4

10

165 ≤ w < 170

1

11

170 ≤ w < 175

0

11

175 ≤ w < 180

1

12

180 ≤ w < 185

0

12

Now I have highlighted the heights of both the year 8 boys and girls I am now going to plot these in individual stem and leaf diagrams, places them both in the same diagram and comparing them. By doing this I can clearly see whether the evidence shown in these diagrams supports my hypothesis:

Stem | Leaf |

120 | 6 |

130 | |

140 | 2 |

150 | 2,5,0,4,5 |

160 | 6,5,2,8,5 |

170 | 0,0 |

180 | 3 |

Stem | Leaf |

120 | 5 |

130 | |

140 | 3 |

150 | 0,2,8,2 |

160 | 2,5,2,2,2 |

170 | 5 |

180 | 3 |

Here are the stem and leaf diagrams I plotted for the heights of the year 8 boys (on the left) and the year 8 girls (on the right). It appears that these diagrams support my first hypothesis being that boys are on average taller then girls but I can’t be sure. To make a clearer comparison I would need to plot a stem and leaf diagram with both the year 8 boys and girls heights, I have done this below:

Leaf | Stem | Leaf |

6 | 120 | 5 |

130 | ||

2 | 140 | 3 |

2,5,0,4,5 | 150 | 0,2,8,2 |

6,5,2,8,5 | 160 | 2,5,2,2,2 |

0,0 | 170 | 5 |

3 | 180 |

1st Hypothesis – Conclusion

By doing this stem and leaf diagram for both the year 8 boys and girls heights, I can clearly note that boys on average do in fact seem to be within the higher sections of the stem and leaf diagram. This meant that I proved my hypothesis was correct that boys would be taller the girls.

2nd Hypothesis - Boys on average weight more then girls

For my next hypothesis, I want to compare another variable amongst boys and girls, this will be like with my first hypothesis but with weight. This hypothesis will be boys on average weight more then girls. Again, like before I will create an accumulative frequency table for both year 9 girls and boys and their weights. I will then plots these in box plots and make a clear comparison of the two to see if it proves or disproves my hypothesis.

Weights of year 9 boys

Weight (kg) | Frequency | Cumulative Frequency |

30 ≤ w < 35 | 0 | 0 |

35 ≤ w < 40 | 1 | 1 |

40 ≤ w < 45 | 1 | 2 |

45 ≤ w < 50 | 3 | 5 |

50 ≤ w < 55 | 4 | 9 |

55 ≤ w < 60 | 1 | 10 |

60 ≤ w < 65 | 2 | 12 |

65 ≤ w < 70 | 0 | 0 |

70 ≤ w < 75 | 0 | 0 |

Weights of year 9 girls

Weight (kg) | Frequency | Cumulative Frequency |

30 ≤ w < 35 | 0 | 0 |

35 ≤ w < 40 | 1 | 1 |

40 ≤ w < 45 | 1 | 2 |

45 ≤ w < 50 | 4 | 6 |

50 ≤ w < 55 | 3 | 9 |

55 ≤ w < 60 | 4 | 13 |

60 ≤ w < 65 | 1 | 14 |

65 ≤ w < 70 | 1 | 15 |

70 ≤ w < 75 | 0 | 0 |

Conclusion

0

85 ≤ w < 90

0

180 ≤ w < 185

0

90 ≤ w < 95

0

This graph slightly supports

My fourth hypothesis as it appears that the heaviest students of the year 11 boys do weigh the most. However other plots on the graph also disprove this and show that even the taller students can way little. To help find more evidence that supports my hypothesis I need to plot another graph for the year 11 girls.

This graph actually appears to disprove my hypothesis clearly, more so then my first graph. This is because it shows that the year 11 girls who are of about average height, weigh the most. To be completely sure of my results however, I will need to do another comparison of the boys and girls with another graph.

Here is my final scatter graph, which plots are colour coordinated so I can clearly see the weights of the year 11 boys (blue) and year 11 girls (blue) and then compare them.

4th Hypothesis - Conclusion

By doing this I found if you include the majority of both the boys and girls of this graph the plots are fairly mixed. This means that the graph shows a variation in both the student’s heights and weights and therefore disproves my fourth hypothesis.

I have now conducted four relevant hypotheses and used individual graphs and tables to test them. My hypotheses were quite different therefore allowing me to use a range of different graphs and methods of comparison. I felt that the evidence I provided for each hypothesis was generally quite clear and easy to understand, therefore making this coursework quite successful.

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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