# maths statistics coursework

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Introduction

Mathematics

Statistics Coursework

Aim

My aim for this project, is to conduct a statistical investigation. I will form some hypotheses and try me to prove or disapprove with them.

For my project, I have been asked to select data about pupils height and weight to see if there was a relationship between the two.

This will then help to develop some lines of enquiry for the statistical investigation.

I will randomly stratify my samples throughout the investigation.

I will then, present my investigation clearly, using scatter graphs, histograms, box-plots and cumulative frequency diagrams. diagrams to help me guide the reader through the process of investigating the data and concluding with the final hypothesis.

Introduction

I am going to use a variety of statistical methods to analyse data, to compare the relationship between weight and height of children from year 7 to year 11.

To help me with my investigation, I have received data from the Mayfield High School. The data consists of 1889 pupils from Year 7 up to year 11. I have decided to take a sample of 20% from each year group as it is a size which is manageable, yet is large enough to provide accurate data that represents the entire population.

The sampling of the data is very important, when looking at such a large amount of the data. It makes the investigation easier and more enjoyable.

There are many sampling possibilities, however, I have decided to look at three of them and choose the most common and effective one.

Systematic Sampling

“If a sample of size s is to be taken from a population of size n, then every n/s member of the population is tested. The starting point is chosen at random.”

Middle

7

F

1.41

39

7

F

1.5

45

7

F

1.66

45

7

F

1.57

45

7

F

1.53

57

7

F

1.62

65

7

F

1.64

47

7

F

1.5

40

7

F

1.5

47

7

F

1.6

47

7

F

1.52

40

Year

Gender

Height

Weight

7

M

1.48

44

7

M

1.6

40

7

M

1.42

26

7

M

1.54

43

7

M

1.63

59

7

M

1.55

38

7

M

1.62

48

7

M

1.43

33

7

M

1.58

59

7

M

1.65

52

7

M

1.62

44

7

M

1.5

50

7

M

1.54

38

7

M

1.42

40

7

M

1.4

40

7

M

1.59

47

7

M

1.53

40

7

M

1.53

38

7

M

1.63

60

7

M

1.65

35

7

M

1.52

38

7

M

1.43

41

7

M

1.52

54

7

M

1.41

31

7

M

1.57

56

7

M

1.5

55

7

M

1.53

40

7

M

1.5

59

7

M

1.62

42

7

M

1.55

32

Year 9 Girls Year 9 Boys

Year | Gender | Height | Weight |

9 | F | 1.52 | 45 |

9 | F | 1.8 | 60 |

9 | F | 1.6 | 48 |

9 | F | 1.58 | 40 |

9 | F | 1.35 | 51 |

9 | F | 1.58 | 50 |

9 | F | 1.56 | 56 |

9 | F | 1.62 | 48 |

9 | F | 1.65 | 72 |

9 | F | 1.68 | 36 |

9 | F | 1.62 | 55 |

9 | F | 1.71 | 54 |

9 | F | 1.2 | 42 |

9 | F | 1.55 | 40 |

9 | F | 1.78 | 59 |

9 | F | 1.52 | 55 |

9 | F | 1.69 | 48 |

9 | F | 1.54 | 47 |

9 | F | 1.65 | 52 |

9 | F | 1.58 | 36 |

9 | F | 1.58 | 36 |

9 | F | 1.63 | 57 |

9 | F | 1.66 | 45 |

9 | F | 1.62 | 42 |

9 | F | 1.6 | 42 |

9 | F | 1.59 | 50 |

9 | F | 1.69 | 48 |

9 | F | 1.52 | 50 |

Year | Gender | Height | Weight |

9 | M | 1.6 | 60 |

9 | M | 1.52 | 52 |

9 | M | 1.8 | 64 |

9 | M | 1.54 | 60 |

9 | M | 1.61 | 45 |

9 | M | 1.75 | 52 |

9 | M | 1.8 | 55 |

9 | M | 1.61 | 62 |

9 | M | 1.61 | 41 |

9 | M | 1.62 | 49 |

9 | M | 1.32 | 38 |

9 | M | 1.58 | 51 |

9 | M | 1.81 | 68 |

9 | M | 1.66 | 46 |

9 | M | 1.48 | 40 |

9 | M | 1.64 | 35 |

9 | M | 2.03 | 60 |

9 | M | 1.72 | 57 |

9 | M | 1.74 | 61 |

9 | M | 1.43 | 60 |

9 | M | 1.64 | 74 |

9 | M | 1.7 | 48 |

9 | M | 1.62 | 42 |

9 | M | 1.67 | 61 |

Year 11 Girls Year 11 Boys

Year | Gender | Height | Weight |

11 | F | 1.68 | 54 |

11 | F | 1.73 | 64 |

11 | F | 1.56 | 50 |

11 | F | 1.68 | 48 |

11 | F | 1.58 | 32 |

11 | F | 1.68 | 47 |

11 | F | 1.75 | 60 |

11 | F | 1.58 | 54 |

11 | F | 1.63 | 52 |

11 | F | 1.68 | 50 |

11 | F | 1.55 | 60 |

11 | F | 1.56 | 45 |

11 | F | 1.58 | 48 |

11 | F | 1.68 | 47 |

11 | F | 1.56 | 38 |

11 | F | 1.78 | 55 |

11 | F | 1.71 | 42 |

Year | Gender | Height | Weight |

10 | F | 1.52 | 45 |

10 | F | 1.67 | 66 |

10 | F | 1.62 | 48 |

10 | F | 1.7 | 48 |

10 | F | 1.73 | 58 |

10 | F | 1.7 | 48 |

10 | F | 1.53 | 65 |

10 | F | 1.8 | 60 |

10 | F | 1.55 | 48 |

10 | F | 1.57 | 48 |

10 | F | 1.57 | 60 |

10 | F | 1.65 | 60 |

10 | F | 1.68 | 58 |

10 | F | 1.61 | 54 |

10 | F | 1.41 | 55 |

10 | F | 1.62 | 46 |

10 | F | 1.7 | 55 |

10 | F | 1.39 | 42 |

10 | F | 1.79 | 45 |

I have grouped the data from Year 7, 8 and 9 into the grouped data tables. From this information I will create various graphs and diagrams. These tables will also help me to organise my data, and make it clearer and neater.

One of the reason why I

Conclusion

As a results of my previous hypothesis, I now believe that my investigation would benefit more, if I was to sample a larger variety of pupils from Mayfield High. This had enriched my investigation for hypothesis, providing a larger representative of the school, therefore than making the results more reliable.

My third hypothesis was aiming to prove that year 7 females will be the lightest in school, whereas the year 11 males will be the heaviest pupils. I have used calculations that resulted in mean and median, as well as the frequency diagrams, box plots and histograms. These were all essential in order to provide enough evidence for my investigation. I have also noticed that my graphs show that, boys appear to be heavier than the girls despite the age group; but when looking at the age, this is not always true.

If I was to carry out this investigation again, I would make few changes before preparing myself to tackle this task. One of them would be to perform a vertical dispersion on my scatter graphs, as this will provide a much more accurate results when looking at the line of the best fit, and enable me to produce a more accurate predictions. Furthermore, I would use a larger sample of data to investigate, a this will let me eliminate more outliers and inaccurate results. In addition the correlation of the coefficient would have resulted in a much stronger relationships. This will then help me to get a better idea whether the correlation for males or females was stronger.

Despite the fact that there are few factors that I would change, if I got a chance to undertake this investigation again, I believe that the Mayfield High School investigation provides a reliable evidence that support my hypothesis.

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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