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Mayfield High School - Relationships between height and weight

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Introduction

E. Fry 5V

Statistics Project

Mayfield High School

Relationships between height and weight

My aim in this project is to investigate any relationships between height, weight and gender. I will investigate this by comparing and analysing data through various means, including tables, charts and graphs.

The total number of students at the school is 1183. It is unfeasible to do a study on all the pupils in the time available. Therefore I decided to take a stratified random sample of the pupils. I did a stratified random sample in order to ensure a fair sample, as there are differing numbers of pupils in each year, so therefore taking the same number from each year is not a good representation of the school community. How I did this is shown on the next page.

Finally I found out how many girls and boys I should sample from each year using:

 No of Yr N boys/girls   x 50image00.png

Total number of pupils

N is the year number, and 50 is the overall size of my sample, therefore I multiplied the result by 50. I chose 50 because it is a manageable size, but it still gives a good representation of the pupils.

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Middle

Therefore the second set of graphs I did were Scatter charts, to see if there was a correlation between height and weight. I expected these to show a strong positive correlation, and both the graphs for boys, and the graph for girls did this. However, the correlation when I put both girls and boys together was weaker than when they were done individually. This was shown by only having a correlation coefficient of 0.467, compared to the boys’ coefficient of 0.572. However, the girls’ had the weakest correlation with a coefficient of 0.288. This weak correlation could be explained by some exceptional values in my data, for example the girl who was 151cm tall, but weighed 65kg. Also, often as girls get older, they become concerned about their figure and diet, so this could affect the correlation as well. The lines of best fit in my diagrams predict that a boy who was 170 cm tall would have a weight of around 59 kg, and a girl who was the same height would weigh around 54 kg.

The third set of graphs I did was the Pie Charts. These were to provide a visual representation of the standard deviation.

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Conclusion

The analysis was subject to some limitations however. The results could be considered more representative if a larger sample of pupils had been taken and some consideration had been given to the ages of students in the sample.

Also, my predictions are based on general trends observed in the data. Within the sample, there were exceptional individuals whose results fell outside the general trend, for example the Year 9 girl who weighed 65kg despite only being 151cm tall.  

If the time were available, I would extend my investigation to consider the relationship between shoe size and weight, not only between genders, but between ages as well. From the work done in this project, I could predict that once age is considered, the correlation between height and weight will be much stronger than when it is not.

Overall therefore, although I feel that the conclusions drawn from the data I have do support my hypotheses, the data are only conclusively proves my hypothesis “that as boys get taller they get heavier.” My research does also show that there is a strong correlation between height and weight.

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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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