# Investigating the relationship between height and weight.

Extracts from this document...

Introduction

## Statistics Coursework

## Hypothesis

In year 7 females are generally taller than males but males are heavier in weight. By year 11 males are taller and heavier than girls.

## Introduction

I will be investigating the relationship between height and weight; I will try to prove the above hypothesis. As my hypothesis suggests I will be using year 7 male and females and year 11 males and females from Mayfield High School.

The information I already know is that females tend to grow sooner and faster than boys their growing rate slows down while males continue to grow on average to a taller height and their weight is also heavier regardless of height.

To begin with I will have to look at the data provided on the Mayfield High School database. Investigating the database I have filtered all necessary data and separated it from the initial data. The form of sampling that I will be using is stratified sampling. This is a good method to avoid bias results.

In year 7 there are a total number of: 282 students

In year 11 there are a total number of: 170 students

Total: 452 students

I will be taking a sample of 100 students for in my investigation:

Year group | Students | Number of students sampling-100 |

7 | 282 | 282/452 x 100 = 62.38938 = 62 |

11 | 170 | 170/452 x 100 = 37.61062 = 38 |

I now know that I need 62 people from year 7 and 38 from year 11. Now I need to find out how many male and female students to make this a fair test.

Year Group | Sex | Number of students sampling from each gender |

7 | Male | 151/282 x 62 = 33.19858 = 33 |

7 | Female | 131/282 x 38 = 28.80142 = 29 |

11 | Male | 84/170 x 38 = 18.77647 = 19 |

11 | Female | 86/170 x 38 = 19.22353 = 19 |

Middle

35 ≤ h < 40

7

10

40 ≤ h < 45

7

17

45 ≤ h < 50

13

30

50 ≤ h < 55

0

30

55 ≤ h < 60

1

31

60 ≤ h < 65

1

32

65 ≤ h < 70

1

33

Weight- Year 7 females | Frequency | Cumulative Frequency |

30 ≤ h < 35 | 1 | 1 |

35 ≤ h < 40 | 2 | 3 |

40 ≤ h < 45 | 16 | 19 |

54 ≤ h < 50 | 7 | 26 |

50 ≤ h < 55 | 3 | 29 |

55 ≤ h < 60 | 1 | 30 |

Conclusion from cumulative frequency graphs (previous page):

In the cumulative frequency graphs for height I can see that the males and females graphs are quite parallel. I calculated the interquartile range from these graphs and results show that the interquartile range for year 7 males is 152.2m and females is 150.75m, the smallest range indicates that much of the data is concentrated about the median. This shows that year 7 males’ height varies a lot.

In the Cumulative Frequency graphs for weight I cans see that the females have a tighter range, most of the females are in the middle half of the graph. There is more variation on the males weight; again this shows that the female’s interquartile range is smaller.

## Box Plots

I have decided to draw box plots to show the interquartile ranges better:

Conclusion from box plots (next page):

The cumulative frequency graph representing height shows us that year 7 females have a higher median, and this tells us that on average females are taller than males.

The females also have a larger gap between that upper quartile and lower quartile ranges this shows that they have more varied height range, whilst the males have a smaller gap. The box plot for weight shows that the interquartile range is bigger for the male students. The median for both the males and females is very similar this shows that males averagely weigh the same amount as the females, although they have a bigger upper quartile so they have a more varied scale.

## Standard Deviation

Using the Excel formula =STDEV (D4:D33) which was given to us by our maths teacher, I calculated the standard deviation of my data.

For year 7 males height the standard deviation is:0.085cm to 3 decimal places.

For year 7 females height the standard deviation is: 0.106cm to 3 decimal places.

The females have a higher standard deviation shows the spread of the values from their mean, therefore the less reliable the data. The standard deviation shows that the males data was closer together and more accurate.

For year 7 boys weight the standard deviation is: 7.79kg to 3 decimal places.

For year 7 boys the standard deviation is: 5.47kg to 3 decimal places.

The males again have a lower standard deviation than the females it is fair to say that my random sampling of males was more reliable than my random sample of female.

#### Year 11

Scatter graphs

From these graphs I can see that the females have poor correlation, the males have better correlation. In both of the graphs the majority of students are in the 1.4 to 2 ranges though the males are more spread out.

The weight scatter graph shows that the females are more close together, widely held within the boundaries of 40 and 60 kg. This scatter graph is even more compact than the year 7 results. The male students are a lot more varied. As I have stated in my prediction the males are heavier by year 11.

I have again produced frequency tables so that I could draw my cumulative frequency graphs to show the following data:

## Frequency graphs

Height- Year 11 males | Frequency | Cumulative Frequency |

150 ≤ h < 155 | 2 | 2 |

155 ≤ h < 160 | 1 | 3 |

160 ≤ h < 165 | 1 | 4 |

165 ≤ h < 170 | 2 | 6 |

170 ≤ h < 175 | 1 | 7 |

175 ≤ h < 180 | 5 | 12 |

180 ≤ h < 185 | 4 | 16 |

185 ≤ h < 190 | 0 | 16 |

190 ≤ h < 195 | 0 | 16 |

195 ≤ h < 200 | 3 | 19 |

Conclusion

Another reason for their height is that boys grow faster than girls at their peak rate. They grow faster because they have higher levels of testosterone in their bloodstream than girls. The testicles release more and more testosterone into the blood stream as they mature. During puberty an average boy's production of testosterone will increase tenfold.’

My hypothesis proved this fact, and I have found that there is a relationship between age, height and weight. This connection can be seen through my graphs. I noticed in my graphs that the females always had a tighter distribution then the males; this shows that males aged between 11-16 vary a lot in terms of height and weight.

Criticisms

In the process of proving my hypothesis I used standard deviation to find out how far my data was from the mean, showing the more accurate data. I could have improved this point by having more people in my sample and this should bring the standard deviation down because there would be more samples which should in theory follow the mean. My scatter graphs could be improved because the points were not very clear and they were too small to interpret. Another improvement that I could have done was to produce all my graphs on the computer so that I have accurate results, but I could not do this, as I did not know how to draw more complex graphs on the computer.

Evaluation

Overall my investigation went quite well because I proved my hypothesis, showing my mathematical skills on; stratified and random sampling, producing graphs and using Excel for my scatter graphs and standard deviation.

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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