# Maths Coursework - Statistics

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Introduction

Mathematics GCSE

Coursework

Introduction

In this data handling project I will analyse and investigate the data from the first form and the fifth form. There is a large population therefore I will have to sample the data by using different techniques and methods in which to shorten the quantity, this will enable me to therefore analyse the data properly instead of investigating the whole data. I will also discuss any problems with the data and show any ways to avoid bias.

I will firstly make hypotheses on the data trying to link similarities and differences. I will investigate this by making suitable calculations such as working out the mean, mode, correlation, etc. as well as calculations I will use graphs which include histograms, cumulative frequency graphs and scatter diagrams. After making these graphs I will analyse the data, suggesting any patterns.

To conclude the project I will evaluate the results and summarise the calculations and graphs as well as discuss the rules of human proportion and whether they apply to either the fifth form or the first form or both.

Hypotheses

My first 3 hypotheses will access whether or not there are any similarities, trends or differences between the first form data and the fifth form data. My next 3 hypotheses will investigate the rules of human proportion. I will then analyse the graphs and the calculations which are made as a result from the hypotheses.

The hypotheses, includes an outline of the plan as well as identifying any potential problems relating to my strategy:

1. H The mean, modal class and median values will be considerably greater for the fifth formers than those of the first formers.

Ho The mean, modal class and median values will not be considerably greater for the fifth formers than those of the first formers.

Middle

24

32

173

172

21

37

178

183

25

44

172

177

23

46

166

168

21

47

158

163

22

50

175

175

23

53

160

145

22

54

185

187

24

56

180

183

23

63

178

179

23

65

184.5

193

23

73

165

161

23

77

182

179

24

81

180

185

24

85

173

177

23

93

185

183

22

95

173

174

23

101

170

178

26

104

190

190

22

106

173

165

22

111

160

180

24

115

171

169

25

125

175

178

21

129

179

183

21

130

174

183

20

135

176

175

21

141

162

172

26

145

169

179

20

151

178

179

26

155

179

178

24

156

186

190

24

160

175

180

22

163

170

162

22

173

182

183

22

178

169

176

22

179

178

177

21.5

185

180

181

22

Below is the list of sampled data from which I received from doing the simple random sample on Microsoft Excel.

Validating my hypotheses

Hypotheses 1:

Modal class interval | Frequency of 1st form height (cm) | Frequency density |

121 – 140 | 4 | 0.2 |

141 – 145 | 6 | 1.5 |

146 – 150 | 10 | 2.5 |

151 – 160 | 13 | 1.4 |

161 – 170 | 7 | 1.1 |

To find the mean of the height for the 5th and 1st formers I can produce a histogram and compare which year group is taller. I have to work out the frequency density to do this I must divide frequency by class width. Below are tables showing the class intervals and a histogram.

Modal class interval | Frequency of 5th form height (cm) | Frequency density |

151 – 170 | 10 | 0.5 |

171 – 175 | 11 | 2.8 |

176 – 180 | 12 | 3 |

181 – 190 | 8 | 0.8 |

The histogram shows that the frequency density values for the 5th form are higher than for the 1st form, which means the mean value is likely to be higher for the 5th form. It also shows that 2, 5th form frequency density bars are over 2, while there are no bars over 2 for the 1st form, this further proves that the 5th form have a higher mean value than the 1st form and their data is more spread out hence a larger range.

To check this I will also pair up the data and find the percentage difference. I will then find the average of this difference and then see if it is or is not within 10% of the proposed hypotheses.

To find the percentage difference, I found the difference from the 2 height measurements form each year group and then divided it by the 5th formers height then multiplied it by 100.

For example for the 1st 2 measurements:

174 - 150 = 24

24 / 174 = 0.1379

0.1379 X 100 = 13.79

I was able to find the average of these differences easily on excel by copying my data onto the excel spreadsheet then, highlighting the column until the next free cell and then clicking on the average function on the tool bar.

The total percentage difference for the height of 1st and 5th formers is 13.52575.

Therefore my H was correct as the percentage difference was above 10%.

I will now look at the median value of the fifth formers and the first formers, to accomplish this I must find the middle value from my sampled data. To achieve this I will put the sampled data into order, putting the highest at the top of the list and the smallest at the bottom of the list. To attain this in excel I will highlight the data, press DATA on the tool bar and press sort – ascending. Then you identify the 20th and the 21st numbers and find the middle value of these two numbers.

For example: the 20th and 21st numbers for the height of the 1st year is 150 and 151, therefore the number in the middle of this two figures is your median value. In this case it is 150.5

The results for the median values are as follows:

1st form = 150.5

5th form = 175

Therefore my H is again true because the difference is above 15cm.

To determine the modal class value, I organised the data into a frequency table and established the most common class interval.

The two tables shown below are those of the 5th form and 1st form.

Modal class interval | Frequency of 1st form height (cm) |

121 – 130 | 1 |

131 – 140 | 63 |

141 – 150 | 16 |

151 – 160 | 13 |

161 – 170 | 7 |

Modal class interval | Frequency of 5th form height (cm) |

151 – 160 | 3 |

161 – 170 | 7 |

171 – 180 | 23 |

181 – 190 | 7 |

Conclusion

The main area which presented a different trend to that expected was the I have proved my hypotheses using several mathematical justifications such as mean, median, lower and upper quartile ranges. However the results are only good as the quality of the data initially provided. The height measurements, are provided by the pupils of an age group between 11 and 16, where there would be a slight tendency to exaggerate their height by a few centimetres.

I have often presented myself to be taller than my actual height therefore I feel this may also be reflected in the sampled data. Also the accuracy of the data may be compromised because almost all pupils appeared to have rounded their height up to the nearest centimetre. Another distortion to the accuracy of the data is that the 1st form boys are 11 at the beginning of the year and the 5th form boys are 15, therefore if the results were taken at the end of the year the members in the 1st form will be 12 and the pupils in the 5th form will be 16. This is significant in terms of percentage because the 11 year olds would have had a higher proportional increase in height than those compared to the 5th formers.

I feel this exercise to be worth while and potentially provide useful information to the audience for issues such as ordering the right size uniforms and shoes in shops for particular age groups. However I strongly recommend that the height measurements are performed independently by teachers at school to ensure accuracy of data. This could hence mean an improvement in the investigation. Using the height, armspan and head height is limited for a clear conclusion and the use of other data such as weight and shoe size could have added benefit to the project.

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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