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  • Level: GCSE
  • Subject: Maths
  • Word count: 7883

An investigation into the relationship between the height and weight of pupils at Mayfield school.

Extracts from this document...

Introduction

Ben Good Maths Coursework An investigation into the relationship between the height and weight of pupils at Mayfield school Introduction Mayfield School is a secondary school of 1183 pupils aged 11-16 years of age. For my data handling coursework I am going to investigate a line of enquiry from the pupils' data. Some of the options include; relationship between IQ and Key Stage 3 results, comparing hair colour and eye colour, but I have chosen to investigate the relationship between height and weight. One of the main reasons being that this line of enquiry means that my data will be continuous (numerical), allowing me to produce a more detailed analysis rather than eye or hair colour where I would be quite limited as to what I can do because the data is discrete. Pre-test We do a pre-test so we can see if there is any correlation between a persons height and weight because if no correlation is present. Then there is not any point in continuing with the investigation. There were many things that could have gone wrong when I was sampling the data. One of them was that I could have got an anomalous result and I did. The anomalous result I got was: 'Student: 914, Seymour Banks, 1.60m, 9kg' Seymour Banks is an anomalous result because he weighs 9kg. I overcame this by ignoring it and picking another pupil instead. I also picked the same pupil three times while randomly sampling. To help me choose the students fairly I chose them randomly on the computer. Female students: Height Weight 1 1.5 45 2 1.48 37 3 1.8 60 4 1.58 54 5 1.59 44 6 1.62 54 7 1.45 51 8 1.58 48 9 1.66 45 10 1.64 47 11 1.56 56 12 1.79 43 13 1.54 42 14 1.75 57 15 1.64 55 16 1.63 52 17 1.58 55 18 1.55 50 19 1.65 48 20 1.68 47 This is a table containing the female results from my random ...read more.

Middle

Mean Modal Class Median Range Boys 164 cm 150-160 cm 162 cm 59 cm Girls 158 cm 160-170 cm 161 cm 53 cm Differing from the results from my weight evidence, the heights' modal classes for boys and girls differ, and much to my surprise the girls' modal class is in fact one group higher than the boys. This is very visible on my frequency polygon as the girls data line reaches higher than that of the boys. This doesn't exactly undermine my hypothesis however as the modal class only means the group in which had the highest frequency, not which group has a greater height. On the other hand the average height supports my prediction as the boys average height is 6 cm above the girls. The median height had slightly less of a difference than the weight as there was only one centimetre between the two, although again it was the boys' median that was higher. When it comes to the range of results, similarly to the weight the boys range was vaster than the girls, although there was no where near as greater contrast in the two with a difference of only 6 cm between the two. To test that my investigation was fair I am going to check for outliers. Boys Lower bounds Q1 - (Q3 - Q1) 152.5 - (180 - 152.5) = 125cm There are no pieces of data that are below the lower bound. Upper bounds Q1 + (Q3 - Q1) 180 + (180-152.5) = 207.5cm There are no pieces of data that exceed the upper boundary. Girls Lower bounds Q1 - (Q3 - Q1) 155 - (166 - 155) = 144cm This means that five of the pieces of data are below the lower bounds and will have to be replaced. Upper bounds Q1 + (Q3 - Q1) 166 + (166 - 155) = 177cm There is no data that exceeds the upper bound limit. ...read more.

Conclusion

When producing the random sample of 60, I felt that was a satisfactory amount to work with as picking up an analysis and producing graphs from this data was simple and done efficiently. Although when it came to the stratified sample, and I was looking at the different age groups using again a sample of 60 trying to represent the school on a smaller scale - I do not feel it was as successful. If I were to repeat or further this investigation - I would definitely use a larger number of pupils for the stratified sample as when the numbers of the school pupils were put on a smaller scale, I only ended up in some cases with a scatter graph with only 4 datum points upon for the year 11 students. To retrieve accurate results from this method of sampling, I feel it is necessary to use a sample of at least 100. Additionally to the stratified work, if I had a larger sample - I would also produce additional graphs, i.e. cumulative frequency/ box and whisker, as I feel that I could draw a better result from these as I felt the scatter diagrams I produced were rather pointless. I feel my overall strategy for handling the investigation was satisfactory, if I had given myself more time to plan what I was going to do I think I would have come up with a better method and possibly more successful project. One of the positive points about my strategy is that because I used a range of samples it meant that I was not using the same students' data throughout - I instead used a range of data therefore maintaining a better representative of Mayfield school as a whole. There is definitely room for improvements in my investigation - if I were to do it again I would expand my planning. Despite that I feel my investigation was successful as it did allow me to pull out conclusions and summaries from the data used. 1 ...read more.

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