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  • Level: GCSE
  • Subject: Maths
  • Word count: 3211

I will investigate whether or not there is a relationship between heights and weights of boys and girls at Mayfield High School. The population of this investigation are the pupils at the Mayfield High School.

Extracts from this document...

Introduction

Mayfield School Statistic Coursework Introduction In this investigation, I will investigate whether or not there is a relationship between heights and weights of boys and girls at Mayfield High School. The population of this investigation are the pupils at the Mayfield High School. Line of Enquiry: Relationship between heights and weights this is because from my own knowledge, I know there is a relationship which I would like to unravel. Also, there is a possibility of it producing some surprising results. Collecting Data I will be taking a random sample of sixty pupils. I am choosing sixty pupils because it will be adequate enough for good graphs/charts and also because it divides into three hundred and sixty exactly which can be useful for some calculations and it has twelve different factors which can make it easier for certain calculations. I will be using a sample because it will be easier to handle. I will sample by assigning a random number to each row/person which can be done by pressing RAN# on the calculator or by typing =RAND() in Microsoft Excel. From these random numbers assigned to each pupil, I can sort this numerically and if I want sixty random samples, I select the top sixty. I will not take too little results so that the results are not reliable and I will not take too many so there are all the points on a graph. Therefore I will take a sample of sixty. This ensures that there is no bias which is useful because it ensures that the data will be accurate. I am taking a sample because it will be easier to handle and makes it a representative sample which means it represents the whole population. I want a representative population so the results represent the whole population, not just the sample, so any conclusions made will relate to the whole population, not the sample in general. ...read more.

Middle

Also, to my knowledge, I know that 4.65m is an impossible height as the Gunniess world record for the tallest person is 2.72m tall. (I could also use the method stated on page one to prove that this is an anomaly/outlier.) This anomaly could be due to a typo or a mistake of legibility or it could be a mischievous pupil. So I excluded the result to get (PTO): (Fact about world's tallest man taken from: http://www.guinnessworldrecords.com/gwr5/content_pages/record.asp?recordid=48409) As you can see, the graph as dramatically changed. The gradient is now 48.282 Year 11 From Microsoft Excel, I have found out that the equation of the line of best fit for the year elevens is y = 51.73x - 32.093. (I have not drawn a graph as the only needed information is the gradient (which is used below)). If I synthesise all the gradients together in a list below so I can analyse them further easier, I get the following table: Year Gradient 7 34.542 8 40.239 9 43.953 10 48.282 11 51.730 As you can see, the gradients which approximately increase uniformly. I have put these onto a graph to see the relationship between them: As you can see on the graph above, the graph gives an extremely strong positive correlation and the line of best fit has a gradient of 4.2419. This means that every year a pupil becomes older, the weight that they increase by when they get 10cm taller increases by 4.24kg every year. However, this approximation/conclusion cannot be true for every single person. From my own knowledge and experience, people grow at different rates and at some point in there lives, they discontinue growing and even shrink. I do not have a sufficient amount of data to go further into this as my population is only pupils at a school which the highest age is sixteen. However, the year group is discreet data. ...read more.

Conclusion

As well as this, I conclude that when the age increased, the weight increased, but the amount that that weight increased by became amplified. This can be related to real-life situations such at the recent obesity crisis. However, as weight can continue to increase after a pupil's teenage years, and from real life experience and my own knowledge, the height cannot be controlled - it usually always stops and sometimes reverses. The weight can be controlled by a pupil consuming more or less which can suggest that there cannot be a fully justifiable conclusion made that can relate to everybody in the population as one of the variables can be directly controlled by a human being and the other variable cannot. However, apart from this, I can conclude that the majority of the population prove that my hypothesis is correct: as the height increases, the weight increases - it is directly proportional. The techniques that I have used in this investigation have been pretty reliable. They have been complimented by the results/the sample of results which have produced accurate data which has been fairly easy to extract detailed, valid conclusions from. I could improve/continue this by extending the problem and separating the data by gender - from my own knowledge, I think that the two different genders grow at different rates. I could have a box and whisker diagram showing how the different heights and weights were distributed throughout the population. However, the conclusions made in this piece of work only directly apply to the Mayfield High School data - the conclusions are limited to the Mayfield High School; however it may coincidently apply to real life as the secondary data is based on a real life school. Also, I took a sample of sixty random pupils each time. This can represent the whole populations, however sometimes it cannot. The majority of the sixty pupils in the sample may all coincidently follow the hypothesis that was being investigated at that particular time. ?? ?? ?? ?? Mathematics Coursework Mr. England Page 1 of 10 ...read more.

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