# In this investigation, I intend to find out whether there is a relationship in height and weight in students, and how this relationship changes between girls and boys, with age.

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Introduction

Neeraj Shah 09/03/04

CONTENTS

- INTRODUCTION………………………………………………………….………………………….………..2

Hypothesis…………………………….…………………………….……………………………………..2 Plan…………………………….…………………………….…………………………….…………………….3 Data Collection…………………………….…………………………….………………………………3 Scatter Graphs…………………………….…………………………….……………………………..5 Spearman’s Rank Correlation Coefficient……………………………………………6 Box and Whisker Diagrams…………………………….……………………………………….7

Stem and Leaf Plots…………………………….…………………………….…………………….7

Body Mass Index…………………………….…………………………….………………………….8

Mean, Median, Mode and Interquartile Range……………………………………8

- RESULTS…………………………….…………………………….…………………………………………………..9
- ANALYSIS…………………………….…………………………….……………………………………………..25

Anomalies…………………………….…………………………….……………………………………..27

- CONCLUSION…………………………….…………………………….………………………………………29
- EVALUATION…………………………….…………………………….………………………………………30
- APPENDIX 1 – Stratified Sample Calculation…………………………….……………..31
- APPENDIX 2– Tables of Data…………………………….………………………………………..33
- APPENDIX 3 – Spearman’s Rank Calculations…………………………….……………...43

INTRODUCTION

In this investigation, I intend to find out whether there is a relationship in height and weight in students, and how this relationship changes between girls and boys, with age. I have chosen to investigate the relationship between the height and the weight as I think that the height and the weight are the only two categories that will give a clear correlation. If I was to investigate the relationship of two other categories, like the eye colour and the IQ, I believe that however interesting and amusing the results would be, they would not provide too clear a relationship, or any conclusive information.

The data provided gives information about 1183 girls and boys at Mayfield High School, who have been categorized into their year groups. These year groups begin with the students entering their teens, and end in their mid-teenage years.

In order to be able to compare girls and boys in each year, I will represent the distribution of heights and weights for both sexes in each year in various forms. I plan to use stem and leaf plots, scatter graphs and box plots, and a wide range of calculated data, like the mean of the heights and weights, their interquartile range and their Body Mass Index.

Middle

143

261

10

106

94

200

11

84

86

170

This gives a total of 1183 students, and I have decided to take a sample of 250 students, to represent them. So to obtain the number of students needed in this sample from each year group, the following calculation is done:

250 * number of students

1183 in Year group

For each individual calculation, please refer to Appendix 1, but to demonstrate this calculation, if we take Year 7 as an example:

250 * 282 = 59.6

1183

This means that 59.6 (60) of the pupils in the sample should be from Year 7. To obtain the number of girls, and the number of boys from each year, the following calculation is done:

Number of Boys/Girls * Number required for sample

Total Number of Students

Again, for each individual calculation, please refer to Appendix 1, but as an example, we take the number of boys required from Year 7:

151 * 60 = 32.1

282

This means that 32.1 (32) boys should be taken from Year 7. After making all these calculations, I obtained the following numbers for each sub-sample:

Year Group | Number of Boys | Number of Girls | Total |

7 | 32 | 28 | 60 |

8 | 31 | 26 | 57 |

9 | 25 | 30 | 55 |

10 | 22 | 20 | 42 |

11 | 18 | 18 | 36 |

To make sure this investigation is fair, the data that will be chosen will have to be randomly picked from all the data. To obtain a completely random set of results, the random number generator on www.random.org will be used, which provides a random sequence of numbers within a given field. This field is determined by two numbers, which in this case, would be the number of the cell, on the excel document providing all the data, that corresponds with the sub-sample in question. So for example,

Conclusion

Scatter Graphs 1 and 2 have been used as they show a positive correlation between height and weight. Scatter Graphs 3 and 4 have been used in together with each other, as Scatter Graph 3 does show a positive correlation between height and weight, but after consulting the stem and leaf plot comparing students in Year 8, and the associated box and whisker diagram, Scatter Graph 4 displays how anomalies can affect the line of best fit, as the various anomalies have been removed from Graph 3, and the graph has been re-plotted, and the Spearman’s Rank Correlation Coefficient has been used to discover whether there actually is a correlation between height and weight in the boys in Year 8, as the points were still quite widely scattered on the graph. Scatter Graph 5 has been included to confirm the findings of the relationship between height and weight.

Boxplot 1 has been included to compare the Body Mass Index of all the students in their various years. Boxplots 2 and 3 have been included to display the change in Body Mass Index for boys and girls separately. Line Graphs 1 and 2 have been included to confirm the findings about the difference in the relationship between girls and boys with age. Boxplots 4 and 5 have been included to display the distribution of heights and weights for all the students. They will be used to find any other anomalous results.

Stem and Leaf Plots 1 and 2 have been included to confirm the anomalies in Scatter Graph 3, but Stem and Leaf Plot 2 has also been included to display the limits of using stem and leaf plots. Stem and Leaf Plots 3 and 4 have been included to single out anomalies displayed by the box and whisker diagrams.

Maths Coursework - Mayfield High School

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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