# Maths Statistics Coursework - relationship between the weight and height

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Introduction

Matthew Eden

Planning

Introduction:

In this investigation, I am aiming to find out information on the relationship between the weight and height and the relationship between the age and height.

Hypotheses:

- As the height increases, the weight increases
- As the age increases, the height increases
- Boys have a higher average height than girls

Justification:

I think that as someone’s height increases, their weight increases. I predict this because of basic knowledge of the human body. As someone’s body grows, it the muscles, bones and fat on the body increases and gets larger. And as these increase, they make the body weigh more. I will present this data in scatter graphs for boys, girls and both. I will use Microsoft Excel to create this graph because I think that it will prevent human error and it will enable me to change the scales or any other amendments at any time with ease. This will help me compare and contrast the different genders’ heights and weights. To give me knowledge of the correct correlation, I will use product-moment correlation coefficient which is a calculation that shows the correlation value of the data. For all the scatter graphs, I will construct them by using Microsoft Excel which will allow me to group the data to present them into scatter graphs.

I predict that as the student gets older, their height also increases for all boys and girls. This is probably because as you get older, you grow which also increases your height. I will simply plot this data in a scatter graph showing the ages and heights, hopefully providing me some correlation which I can interpret.

Also, I think that all boys will be taller than all the girls in all the year groups in the school.

Middle

0.5202

1.60

49

-0.01

-0.8

0.000081

0.64

0.0072

1.55

45

-0.06

-4.8

0.003481

23.04

0.2832

1.53

52

-0.08

2.2

0.006241

4.84

-0.1738

1.49

52

-0.12

2.2

0.014161

4.84

-0.2618

1.66

45

0.05

-4.8

0.002601

23.04

-0.2448

1.71

35

0.10

-14.8

0.010201

219.04

-1.4948

1.59

52

-0.02

2.2

0.000361

4.84

-0.0418

1.40

41

-0.21

-8.8

0.043681

77.44

1.8392

1.65

45

0.04

-4.8

0.001681

23.04

-0.1968

1.80

48

0.19

-1.8

0.036481

3.24

-0.3438

1.60

40

-0.01

-9.8

0.000081

96.04

0.0882

1.80

42

0.19

-7.8

0.036481

60.84

-1.4898

1.67

48

0.06

-1.8

0.003721

3.24

-0.1098

1.65

54

0.04

4.2

0.001681

17.64

0.1722

1.58

45

-0.03

-4.8

0.000841

23.04

0.1392

1.65

45

0.04

-4.8

0.001681

23.04

-0.1968

1.52

47

-0.09

-2.8

0.007921

7.84

0.2492

1.60

9

-0.01

-40.8

0.000081

1664.64

0.3672

1.85

62

0.24

12.2

0.058081

148.84

2.9402

1.65

55

0.04

5.2

0.001681

27.04

0.2132

1.50

50

-0.11

0.2

0.011881

0.04

-0.0218

1.65

54

0.04

4.2

0.001681

17.64

0.1722

1.69

42

0.08

-7.8

0.006561

60.84

-0.6318

1.70

54

0.09

4.2

0.008281

17.64

0.3822

1.67

48

0.06

-1.8

0.003721

3.24

-0.1098

1.91

82

0.30

32.2

0.090601

1036.84

9.6922

1.62

63

0.01

13.2

0.000121

174.24

0.1452

2.06

84

0.45

34.2

0.203401

1169.64

15.4242

1.63

59

0.02

9.2

0.000441

84.64

0.1932

Average = 1.61

Average = 49.8

0.962850

9550.00

46.8

Result for Correlation = 0.488050598

With this result for the correlation for all the boys and girls in the sample, I have gathered that there is a relatively positive correlation because it is about the middle between 0 and 1 which is neither a no correlation nor a very strong correlation. I have to consider that there are a couple anomalies which could have possibly distorted the means which could in turn alter the PMCC for the whole of the high school.

This graph and calculations have aided me to conclude on my hypothesis including ‘as the height increases, the weight increases.’ This is a basic hypothesis which can be proved by using this scatter graph which clearly illustrates the relationship between the two variables.

This is a scatter graph displaying the heights and weights for all the boys.

There is a definite correlation for these variables; however, there are a few anomalies which are probably mistakes which happened when entering the data. Since product-moment correlation coefficient allows me to view how much this set of data is positive or negative, I will use this to see how positive the relationship is between the variables.

All Boys | ||||||

Height (m) (x) | Weight (kg) (y) | x- | y- | (x-)^2 | (y-)^2 | (x-)(y- |

1.47 | 50 | -0.16 | 0.8 | 0.026244 | 0.64 | -0.1296 |

1.52 | 32 | -0.11 | -17.2 | 0.012544 | 295.84 | 1.9264 |

1.65 | 52 | 0.02 | 2.8 | 0.000324 | 7.84 | 0.0504 |

1.53 | 40 | -0.10 | -9.2 | 0.010404 | 84.64 | 0.9384 |

1.57 | 48 | -0.06 | -1.2 | 0.003844 | 1.44 | 0.0744 |

1.55 | 38 | -0.08 | -11.2 | 0.006724 | 125.44 | 0.9184 |

1.72 | 51 | 0.09 | 1.8 | 0.007744 | 3.24 | 0.1584 |

1.66 | 43 | 0.03 | -6.2 | 0.000784 | 38.44 | -0.1736 |

1.32 | 47 | -0.31 | -2.2 | 0.097344 | 4.84 | 0.6864 |

1.32 | 48 | -0.31 | -1.2 | 0.097344 | 1.44 | 0.3744 |

1.60 | 49 | -0.03 | -0.2 | 0.001024 | 0.04 | 0.0064 |

1.55 | 45 | -0.08 | -4.2 | 0.006724 | 17.64 | 0.3444 |

1.65 | 45 | 0.02 | -4.2 | 0.000324 | 17.64 | -0.0756 |

1.80 | 48 | 0.17 | -1.2 | 0.028224 | 1.44 | -0.2016 |

1.60 | 40 | -0.03 | -9.2 | 0.001024 | 84.64 | 0.2944 |

1.80 | 42 | 0.17 | -7.2 | 0.028224 | 51.84 | -1.2096 |

1.67 | 48 | 0.04 | -1.2 | 0.001444 | 1.44 | -0.0456 |

1.60 | 9 | -0.03 | -40.2 | 0.001024 | 1616.04 | 1.2864 |

1.85 | 62 | 0.22 | 12.8 | 0.047524 | 163.84 | 2.7904 |

1.65 | 55 | 0.02 | 5.8 | 0.000324 | 33.64 | 0.1044 |

1.50 | 50 | -0.13 | 0.8 | 0.017424 | 0.64 | -0.1056 |

1.91 | 82 | 0.28 | 32.8 | 0.077284 | 1075.84 | 9.1184 |

1.62 | 63 | -0.01 | 13.8 | 0.000144 | 190.44 | -0.1656 |

2.06 | 84 | 0.43 | 34.8 | 0.183184 | 1211.04 | 14.8944 |

1.63 | 59 | 0.00 | 9.8 | 0.000004 | 96.04 | -0.0196 |

Average = 1.63 | Average = 49.2 | 0.657200 | 5126 | 31.84 | ||

Result for Correlation = 0.548573697 |

There is a relatively strong positive correlation for all the boys.

Conclusion

Problems and Limitations

One problem involving the statistical calculations was that I calculated the upper, lower, median and inter-quartile range because I simply forgot that I have to work out 25th, 50th and 75th percentile of the values, so therefore, I went back to those calculations and fixed them. This led to me constructing another box and whisker plot for these averages because they were wrong.

One main limitation is that I could have sampled from a large population. Instead of sampling from 50 students, I think that if I had more time to do this investigation, I would suggest to myself to sample from the entire school or collect a census report to fully reflect a large population. This would allow me to justify the data more accurately and produce better relationships to prove my hypotheses.

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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