Maths Data Handling
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Introduction The line of enquiry that I have chosen is 'The relationship between height and weight'. To investigate this line of enquiry, I am using secondary data (that I will acquire from the internet) so that there will be no bias and unfairness that is obtained through the collection of primary data in questionnaires. The data that I am using is on a fictitious school, Mayfield High School, but the actual data has been obtained from a real school. This is useful as there will be five age groups that are considered in the whole investigation. However the age groups that lie below the age of 11 and age groups that lie over the age of 16 will not be thought of in the investigation as it stretches out of the age boundary in Mayfield High School. There are 1183 pupils in Mayfield High School and I will be using the following pieces of data on each pupil: - year group, age, gender, height and weight. This means that I will have a total of 5915 datum points to work from. This is obviously too large so I will use a sampled piece of data of 100 pupils. Since I will be using stratified sampling I will need to know how many boys and girls there are in each year. The table below shows the exact figures. Year Girls Boys Total 7 131 151 282 8 125 145 270 9 143 118 261 10 94 106 200 11 86 84 170 I will need this table throughout my investigation so that I can construct a stratified sample. This is because I will need to know how many girls and boys there are and the number of students in each year. This will enable me to construct a fair sample, where there will be proportionate numbers of students in the sample to the actual number of students in each year.
To improve the results I got and strengthen them, I could extend the random sample, or even repeat this experiment with a completely different random sample of 50. My conclusion is reliable as the results clearly show that there is a positive correlation between height and weight. However, the plotted points are a little spread out, which makes it a little bit difficult to spot a clear trend. Although the line of best fit fixes this, the overall conclusion could be argued as unreliable. This means that there should be another way that the correlation can be made even better in a scatter diagram. This is where the factor of gender should be considered. The sample could have been slightly biased if more girls were randomly selected than boys, or if it was the other way round. This is because in the scatter diagram, it could be difficult to find a line of best fit because of all the different heights and weights that are affected by gender. However, the purpose of this part of the investigation was to explore the hypothesis of: 'In general, the taller a person is, the heavier that person is likely to be'. This was answered as true and so we now know that there is this correlation between height and weight. This can lead on to another extension to the line of enquiry, where a new hypothesis should be tested that involves gender. This is that: 'There will be a better correlation between height and weight if boys and girls are considered separately'. Further Investigation Hypothesis > There will be a better correlation between height and weight if boys and girls are considered separately. Plan In the early section of this investigation, or, in other words the pre-test, evidence was found that suggested that height and weight were both affected by gender. I am now trying to show that there is a better correlation between height and weight if girls and boys are considered separately.
This means that the heights for the boys population in the sample were more spread out about the mean than it was for the heights for year 7 boys. This strongly suggests that there is a much stronger correlation between height and weight when age is considered. Along with this, the earlier part of the investigation suggested that there was a better correlation between height and weight if boys and girls are considered separately. The general comparison that was found between girls and boys was that in general, boys are taller and heavier than girls. If all this is linked together, a final summary sentence can be said: There is a strong correlation between height and weight if gender and age are considered. Once studied, it is found that in general, boys are taller and heavier than girls. Throughout this investigation I have found that there is a positive correlation between height and weight both across the school and within each year group. The correlation appears to be much stronger when individual year groups and separate genders are considered. However, I can only support this through the experiment that was done with the year 7 boys compared to the boys in the whole school. If I was to improve my investigation, I would investigate each year group and gender, but this would probably be predictable and I think that I have reliable results from the 10% sample of year 7 boys that can support this conclusion. I have to remember that the school is only a small population in the world. There are many other factors that affect height and weight such as the lifestyle of people and another possible factor could be the amount of money that a person earns that affects weight. Specifically in the school, there are factors that affect the correlation between height and weight such as the distance away from school and the mode of transport used to get to school. If a person walks to school, he or she is more likely to be lighter in weight than a person who frequently comes to school by car.
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