# As the height increases the weight increases and also the relationship between these the height and the weight will become stronger as they get older. I also think that there will be a difference in this between the boys and the girls.

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Introduction

Maths GCSE Handling Data Coursework

Mayfield High School – Year 10 & 11

For my statistics coursework I am going to investigate the relationship between the height and the weight. I will use a wide range of mathematical techniques to present my data and findings in different ways. I will also focus to test my hypothesis which is: As the height increases the weight increases and also the relationship between these the height and the weight will become stronger as they get older. I also think that there will be a difference in this between the boys and the girls.

The table below shows the number of boys and girls there are in each year group:

Year Group | Number Of Boys | Number Of Girls | Total |

10 | 106 | 94 | 200 |

11 | 84 | 86 | 170 |

Total | 190 | 180 | 370 |

For my project I will take a random sample of 30 students. I will use the random sample button on a calculator to do this.

Middle

60

I am going to check if there are any outliers in this sample because outliers may change your whole result.

I am using standard deviation to check for anomalies.

The equation for standard deviation =

Where is the mean of the data set and n is the number of values.

Mean = 1.80+1.80+1.80+1.80+1.75+1.75+1.75+1.72+1.72+1.72+1.71+1.70+1.68+1.67+1.65+1.65+1.63+1.62+1.62+1.62+1.61+1.61+1.60+1.58+1.57+1.57+1.55+1.55+1.55+1.52/30

Tally chart for the height

Height is a continuous data, so you need to use class intervals. I’ve used a class interval of 0.05 m.

Height (cm) | Tally | Frequency |

1.50≤H<1.55 | I | 1 |

1.55≤H<1.60 | IIII I | 6 |

1.60≤H<1.65 | IIII II | 7 |

1.65≤H<1.70 | IIII | 4 |

1.70≤H<1.75 | IIII | 5 |

1.75≤H<1.80 | III | 3 |

1.80≤H<1.85 | IIII | 4 |

Tally chart for the weight

Weight is also a continuous data; the class interval I’ve used is 5kg.

Weight | Tally | Frequency |

35≤W<40 | II | 2 |

40≤W<45 | I | 1 |

45≤W<50 | IIII | 4 |

50≤W<55 | IIII I | 6 |

55≤W<60 | IIII I | 6 |

60≤W<65 | IIII I | 6 |

65≤W<70 | II | 2 |

Conclusion

45

1.63

44

1.62

52

1.73

50

1.60

38

1.73

45

1.60

47

1.60

50

1.65

54

1.65

54

1.68

59

1.80

60

1.60

51

1.65

54

1.80

72

1.55

48

1.75

68

1.51

36

1.72

54

1.63

52

1.81

54

1.66

45

1.82

57

1.62

48

1.68

72

1.70

60

1.54

76

1.55

60

1.50

35

1.80

60

1.62

72

1.62

48

1.62

50

1.52

45

1.73

50

1.67

48

1.52

38

1.62

38

1.84

78

1.65

52

1.75

57

1.52

70

1.61

56

1.68

47

1.80

63

1.41

55

1.57

54

1.78

55

1.52

45

1.65

59

1.78

37

1.60

54

1.63

50

1.80

74

1.80

68

1.57

45

For this sample I am going to test whether there is an outlier, because the outlier may change the whole result.

A piece of data is considered an outlier if it is more than two standard deviations away from the mean of the data set.

The mean for the height of boys sample is:

1.63+1.77+1.32+1.62+1.60+1.60+1.65+1.68+1.60+1.80+1.75+1.72+1.81+1.82

To compare my correlation I am going to use product momentum correlation coefficient. This is the accurate way to compare the correlation. It uses the mean of each set of data and looks at the distance away from the mean of each point.

The Formula is

Where and are the means of the x and y values respectively

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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