# This coursework is about a statistical analysis to investigate the height and weight of pupils within Mayfield High School

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Introduction

Introduction

This coursework is about a statistical analysis to investigate the height and weight of pupils within Mayfield High School. The total number of pupils in the school is 1183 but I don’t have time to collect all the heights and weights of all the students so I obtained a random stratified sample of 200 students. I acquired this random stratified sample of 200 pupils by calculating the percentage of male and female in each year group and used the data to form the proportion of students I would take in the sample from each year group. When I attained the percentages of each year group I found that I had to round them up so I could get the whole numbers of pupils instead of having half a pupil and three-quarters, for example, I had to round up 10.6% to 11%, but in the end I still made it up to 100%.

The working out looked like this:

Yr | Gender | Pupils | Percentage for 200 | Proportional Sample |

7 | f | 131 | 11% | 22 |

8 | f | 125 | 11% | 22 |

9 | f | 144 | 12% | 24 |

10 | f | 94 | 8% | 16 |

11 | f | 86 | 7% | 14 |

f | Tot. 579 | 49% | 98 | |

7 | m | 151 | 13% | 26 |

8 | m | 145 | 12% | 24 |

9 | m | 117 | 10% | 20 |

10 | m | 106 | 9% | 18 |

11 | m | 84 | 7% | 14 |

m | Tot. 604 | 51% | 102 | |

M and F | Tot. 1183 | 100% | 200 |

In selecting my data I found that there were errors in the database e.g. I found 3 female students in year 7 all weighing between 110kg and 140kg and I also found that there were 4 students weighing under 10kg – lighter than a sack of rice.

I also found some outrageous heights.

Hypotheses

- As height increases, weight increases
- Boys are naturally taller that girls

Middle

Fig 1.4

From what I have read, predictions are probably even better if we separate the genders so this is what I will do next.

Data separated for Girls and Boys

I will use the same process that is, enter data and used the program Autograph to plot a scatter graph.

These are my results for girls.

For the correlation coefficient of this data, I used the function button in Excel.

These are my results for boys.

Perhaps to get a better correlation coefficient the data also needs to be separated by age.

Data in groups: yr 7 and 11, separated for Girls and Boys

Year 7 girls.

Year 7 boys.

My response to hypothesis 1, that weight increases as height increases is that, it is true. However, the correlation

Coefficient shows that the relationship is variable between the sexes and for individual age groups. I am not going to go any further in this line of exploration because the data is so unpredictable and it’s driving me insane.

But I will look at the average height of the boys and girls.

Boys are naturally taller than girls

I believe that boys are naturally taller than girl so I will conduct tests to see whether my hypothesis is right or not. I will first get the averages for all the boy/girls in each year by obtaining the total heights and then dividing it by the number of pupils.

Conclusion

Using excel I worked out percentages and entered them onto the autograph data sheet.

There are still more boys who are 1.56 metres or less than there are girls. The heights of boys’ fall into a smaller range than the height of the girls’. As this range is probably important I am going to compare the distribution of heights once again but this time using box and whisker diagrams.

It box and whisker diagram shows that girls (yellow) have both a wider range and wider inter-quartile range of heights than do the boys (blue). The advantage of the box and whisker diagram is that it deals with sample proportions (quarters/quartiles). It doesn’t matter how big or small each sample is.

Now that I know that boys are taller than girls I can now predict that boys are heavier than girls so I will make a table and find the mean for them to see if I am right.

Female Year | Total Weight | No. pupils in year | Average |

7 | 978 | 22 | 44.455 |

8 | 1072 | 22 | 48.727 |

9 | 1274 | 24 | 53.083 |

10 | 747 | 16 | 46.688 |

11 | 632 | 14 | 45.143 |

Male Year | Total Weight | No. pupils in year | Average |

7 | 1124.5 | 26 | 43.25 |

8 | 1072 | 24 | 44.667 |

9 | 1012 | 20 | 50.6 |

10 | 988 | 18 | 54.889 |

11 | 869 | 14 | 62.071 |

From this data I am sadly mistaken and I now see that girls are heavier than boy from year 7-9 but after that boys are heavier than girls. So over all girls are heavier than boys for a certain point but boys are heavier in the long-run.

As age increases, the rate of growth decreases

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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