# Investigate the relationship between height and weight.

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Introduction

Data Handling

Introduction:

For my investigation I am using data from a simulated school called Mayfield High School. This is a mixed secondary school with 265 students. There are 2-year groups, 10 and 11. This contains many different records, including, first name, surname, height, weight, age, month of birth, gender, IQ, distance between home and school, and Ks2 result. I have chosen to investigate the relationship between height and weight, because it is quite probable that they influence each other. Here are my hypotheses, which are all related to height, weight or both.

- There will be a positive correlation between height and weight of both years.

- To investigate if students of year 10 are heavier then year 11.

- To find out if students in year 11 are taller.

.

I will collect data on the height and weight of 50 students from both years. I will do a random stratified sample. After every four students I will pick one. I will investigate these hypotheses by drawing scatter graphs cumulative frequency graphs.

I

Middle

72

31

1.85

73

32

1.68

48

33

1.88

75

34

1.6

38

35

1.65

54

36

1.8

72

37

1.65

54

38

1.62

63

39

1.81

54

40

1.68

50

41

1.69

54

42

1.70

63

43

1.68

56

44

1.71

54

45

1.70

60

46

1.92

45

47

1.84

78

48

1.67

52

49

1.72

51

50

1.73

47

Analysis for this graph:

In this graph I can see the points are close to the line and slope upwards. In this case my hypothesis was right, as I have mentioned in my prediction an increasing in height will increase the weight of students. In this case my prediction was right.

Weight:

I will investigate whether the students of year 10 are heavier then the students in year 11. To do this I will draw a cumulative frequency table and then graph. Then I will draw a box plot.

##### Weight of 50 students in year 10

70 | 56 | 56 | 52 | 59 | 64 | 50 | 72 | 54 | 55 |

70 | 57 | 65 | 57 | 65 | 72 | 45 | 63 | 45 | 36 |

56 | 58 | 57 | 40 | 50 | 48 | 62 | 60 | 60 | 72 |

66 | 57 | 55 | 50 | 51 | 36 | 50 | 45 | 47 | 56 |

60 | 54 | 60 | 56 | 48 | 59 | 40 | 80 | 48 | 56 |

Weight (kg) | Tally | Frequency (F) | Mid-interval value, X | FX | Cumulative Frequency |

35≤ w <40 40< w <45 45≤ w <50 50≤ w <55 55≤ w <60 60≤ w <65 65≤ w <70 70≤ w <75 75≤ w <80 80≤ w <85 | 2 2 9 6 15 7 3 5 0 1 | 38 43 48 53 58 63 68 73 78 83 | 76 86 432 318 87 441 204 364 0 83 | 2 4 13 19 34 41 44 49 49 50 | |

50 | 2092 |

##### Weight of 50 students in year 11

36 | 44 | 54 | 60 | 48 | 58 | 54 | 50 | 50 | 56 |

51 | 72 | 54 | 45 | 68 | 58 | 50 | 35 | 60 | 63 |

92 | 45 | 50 | 48 | 84 | 84 | 54 | 44 | 64 | 72 |

72 | 48 | 75 | 38 | 54 | 72 | 54 | 63 | 54 | 50 |

54 | 63 | 56 | 54 | 60 | 45 | 78 | 52 | 51 | 47 |

Weight (kg) |

Conclusion

1.85≤ h <1.90

1.90≤ h <1.95

1.95≤ h <2.00

2

4

10

10

10

3

6

2

1

2

1.53

1.58

1.63

1.68

1.73

1.78

1.83

1.88

1.93

1.98

3.05

6.30

16.25

16.75

17.25

3.56

10.95

3.75

1.925

3.95

3

7

17

27

37

39

45

47

48

50

50

84.75

Hypothesis 3:

I think the students in year 11 are taller then students in year 10. This is because I think the older you are the taller you are.

Analysis for this graph:

The cumulative frequency I have drawn shows the height of students in year 10 and year 11. By looking at it at glance I can see the students in year 11weight more then students in year 10. The curve from the graph are very similar they only different in length.

The box plot shows that the students in year 11 the median is 1.695 whereas in year 10 the median is 1.68.

Year 10:

Median = 1.68

###### Upper Quartile = 1.75

###### Lower Quartile = 1.595

###### Inter Quartile Range = Upper Quartile – Lower Quartile

= 1.75 – 1.595

= 0.155

Year 11:

Median = 1.695

###### Upper Quartile = 1.715

###### Lower Quartile = 1.63

###### Inter Quartile Range = Upper Quartile – Lower Quartile

= 1.715– 1.63

= 0.085

Conclusion:

I think my project has gone well, and I have fulfilled my investigation to prove correct or incorrect from my hypotheses. But although my sample was large enough to come to a reasonable conclusion, as to whether my hypotheses were correct or incorrect, for my results have been more to foolproof, I think I’ve choose large number of data to make it fair sample.

I think my hypotheses were accurate almost.

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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