# The purpose of this investigation is to find if there is any correlation between two variables extracted from 5% random sampling of the Mayfield Data provided.

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Introduction

GCSE Statistics Coursework - Mayfield Data Title: The purpose of this investigation is to find if there is any correlation between two variables extracted from 5% random sampling of the Mayfield Data provided. Introduction: In this GCSE coursework, I will be trying to prove three hypotheses, by using statistical techniques we have learned throughout the GCSE course. My line of enquiry will be based on the relationship between a pupil's IQ and various Key Stage 2 results. I will consider using methods such as histograms (or bar charts), box-and-whisker plots, mean, median, mode, standard deviation, scatter diagrams, product-moment correlation coefficient (PMCC), quartiles and various diagrams to represent the data - depending on which of those is suitable for my hypothesis. After the collected data is analysed, the method is explained and I will explain why I have chosen to use that particular technique. Upon each method, I should be able to draw a conclusion on whether or not there is a correlation between the data I have chosen to compare. In order for the coursework to be improved for further investigations, the evaluation at the end will suggest ways of improving the method used, or perhaps choosing to use another (more suitable) ...read more.

Middle

113 12769 4 16 452 41 108 11664 5 25 540 42 90 8100 3 9 270 43 101 10201 4 16 404 44 102 10404 4 16 408 45 89 7921 3 9 267 46 102 10404 4 16 408 47 91 8281 4 16 364 48 90 8100 3 9 270 49 106 11236 4 16 424 50 100 10000 4 16 400 51 105 11025 4 16 420 52 101 10201 4 16 404 53 103 10609 5 25 515 54 101 10201 4 16 404 55 87 7569 3 9 261 56 100 10000 4 16 400 57 126 15876 6 36 756 58 104 10816 5 25 520 59 78 6084 2 4 156 60 104 10816 4 16 416 61 98 9604 5 25 490 62 97 9409 4 16 388 63 106 11236 5 25 530 Total 6347 645523 255 1073 26078 Scatter diagram I have chosen to use the scatter diagram because it can compare two sets of data and find out if there is any correlation between them. From this diagram below, there is a clear positive correlation between a pupil's IQ and their KS2 mathematics results. These two variables are related since a person's intelligence quotient will affect their performance at certain subjects that require mind work. ...read more.

Conclusion

Both the scatter diagram and PMCC was suitable for this hypothesis, as it gave a clear indication of the correlation. Appendix Estimated Standard Deviation Standard deviation is a measure of how widely values are dispersed from the mean. Since we used the random sampling method, therefore estimated standard deviation is used, which is based on the 5% sample. The larger the dispersion of the data, the larger the value of the standard deviation. One disadvantage of the standard deviation is that it is more difficult to determine compared to other measures of dispersion and extreme values may have an affect the result as the deviation from the mean is squared. The standard deviation method is calculated using the 'non-biased' or 'n-1' method. Estimated standard deviation uses the following formula: Product Moment Correlation Coefficient Although the scatter diagram will determine whether two variables are correlated, you have no measure of the strength of this correlation. The product moment correlation coefficient (PMCC) will give an indication of the strength of correlation. The formula below is used: Mean The mean will give an indication of the average value in a set of data values. Although it gives the average, this can definitely be misleading as it takes into account all the extreme values. Nonetheless, the following formula is used: Edexcel GCSE Mathematics Coursework - Dispatch 1 Syllabus 1388 (H) -Mayfield High School Michelle Lee Reference No. 006134 1 ...read more.

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