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To investigate any relationship between height and foot size in adolescents, aged 7 to 16 years.

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Maths Statistics Coursework

Sarah Fergusson


I was initially given a secondary set of data, with results of a number of questions, which were answered by 1600 students. 721 were in KS2, 642 in KS3 and 237 in KS4.

The first problem I was faced with was to decide which pieces of data I would use, as there were 25 questions asked. I need to use data which is continuous, to get the best use of my results. For example, if I were to use car colour and shoe size, I would not be able to do very much with the information I had. Car colour can only be red, blue, white, etc, and show size can only be size 1-12, etc.

However, with time and height, the data is continuous, as a person can be 125.5 cm tall, not just 125 or 126, for example. After considering this, I have decided to investigate foot size and height.


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As my population is so large (1600), I need to take a sample of it. To be fair, unbiased and effective, this sample needs to be representative of the whole population. It also needs to be large enough for me to draw any fair conclusions from it. It also must be large enough so I can discount any member of the population who seems anomalous, like someone over 3m tall, as they have probably entered false details.

After taking this into consideration, I have decided to take a random stratified sample.

I decided to take the first member of the population, then every 50, up to 1551, giving me 32 pieces of data in my sample.

However, two members of this sample did not answer the “height” question, which is needed for my investigation. So, I have decided not to include these results, taking my sample down to 30.

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The sample population includes data from both boys and girls, of a wide range of ages. An 8 year old is, on average, shorter than a 12 year old, so this has to be kept in mind.

Appendix 1

Looking at the number of boys and girls

My sample contains data from both boys and girls, so I need to look at the sample, to see if the number of boys compared to girls is roughly equal.





This table shows that there are four more girls than boys. This is probably not enough to make a difference to the initial correlation, however it may do. The sample is slightly biased. I need to take into account that boys may grow faster, or slower, than girls, so this would affect the overall result.

So, I need to change my sample, so it is unbiased. After considering all possibilities, I have decided to only use boys in my second sample.

...read more.

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