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Maths Statistics Coursework

Extracts from this document...

Introduction

Maths Statistics Coursework An Investigation into the Relationship between Various Statistics for a School Census Aims/Hypotheses * I am going to try and find out whether on average, boys in year 9 of school will be taller than girls in year 9 of school. I predict that on average boys in year 9 will be taller than girls in year 9, because on average, males are taller than females. * I am going to try and find out whether on average, children in year 7 will have smaller feet than children in year 11. I predict that children in year 7 will have smaller feet than children in year 11, because as you grow older your feet become larger. * I am going to find out whether there is a correlation between the circumference of a child's wrist and the circumference of their thumb. I predict that there will be a weak positive correlation between the two, because if you have large wrists you are likely to have large thumbs as well. My Plan I am going to use all secondary data for this investigation, because collecting the data myself to get primary data would be far too time-consuming and I would have design a questionnaire to do this. All of my data will be obtained from a website, www.censusatschool.ntu.ac.uk, which is an international survey of school children. I have used the random data selector provided by the site to select some sample data (about 2500 records) to use and transferred this to a spreadsheet. Since my data is all secondary, there is no need for me to do any pilot tests to check that the questionnaire works, as I do not have a questionnaire. I will be using 50 pieces of data from the sample for the testing of each hypothesis. After I have randomly selected the 50 records that I am going to study from each set of data, I will tabulate them and find such things as the inter-quartile range ...read more.

Middle

I used this same method of finding outliers for year 7 foot size, year 11 foot size, wrist circumference and thumb circumference. Below are the results I got, and the outliers I found have been highlighted in the table above. Year 7 foot size- Median: 23 Lower Quartile value: 21.75 Upper Quartile value: 25 Inter-Quartile Range: 3.25 1.5*IQR: 4.875 Year 11 foot size- Median: 25.5 Lower Quartile value: 23 Upper Quartile value: 27.5 Inter-Quartile Range: 4.5 1.5*IQR: 6.75 Wrist Circumference- Median: 160 Lower Quartile value: 147.5 Upper Quartile value: 170 Inter-Quartile Range: 22.5 1.5*IQR: 33.75 (No outliers) Thumb Circumference- Median: 60 Lower Quartile value: 40 Upper Quartile value: 67.5 Inter-Quartile Range: 27.5 1.5*IQR: 33.75 (No outliers) Data Analysis and Interpretation Hypothesis 1: I firstly produced the new table for year 9 male and female heights, which excludes the outliers and is in ascending order. Number Year 9 Male Height (cm) Year 9 Female Height (cm) 1 132 153 2 135 153 3 143 154 4 143 155 5 148 155 6 150 156 7 150 156 8 155 157 9 156 157 10 156 158 11 157 159 12 159 159 13 159 159 14 159 159 15 160 160 16 160 160 17 161 160 18 162 160 19 162 160 20 162 161 21 162 162 22 163 163 23 165 163 24 165 163 25 165 164 26 167 164 27 167 164 28 169 164 29 169 164 30 170 164 31 170 164 32 170 164 33 171 165 34 172 165 35 173 165 36 173 166 37 175 166 38 175 169 39 175 170 40 176 170 41 178 170 42 178 171 43 179 172 44 180 173 45 180 175 46 181 47 187 I then grouped the data into groups of varying sizes, and I used 8 groups as I feel that more would be too many but less would make the histogram too simplistic. ...read more.

Conclusion

I used the formula rs = 1-((6?d�)/(n(n�-1))) to work this out, and the result that I produced was rs = 0.5768. Using a critical values table for Spearman's Rank Correlation Coefficient (shown below), I saw that there was no correlation between my data, as 0.5768 is not greater than 0.7647 or less than -0.7647. Sample Size Spearman's 40 -0.736 0.736 50 -0.7647 0.7647 60 -0.7856 0.7856 Should there have been a correlation, I would have drawn a line of regression on my scatter diagram, however as there is no correlation I will not. Therefore, my hypothesis has been shown incorrect, as there is no correlation between the Wrist Circumference and the Thumb Circumference, not even a weak one. Conclusion In summary, the first two of my hypotheses have been proven correct as shown by the graphs and calculations done in the Hypothesis 1 and Hypothesis 2 sections, however my third hypothesis was proven incorrect as shown by the graphs and calculations in the Hypothesis 3 section. In conclusion, I feel that I have successfully investigated the various statistics from the school census and have come to the conclusions shown in my investigations above. Limitations and Extensions The main limitation that I faced during this investigation was time, and I feel that should I have had more time I could have investigated my hypotheses further, and come up with other hypotheses to test regarding the school census. Some extensions that I could attempt in the future include redoing the testing of my hypotheses using much larger samples of data (200 or more) to build up a more accurate picture of the data, attempting different types of graphs to compare and show the data (such as cumulative frequency graphs), and using similar methods that I have portrayed in my investigation above to test other variables from the census (such as height of belly button). ?? ?? ?? ?? 1 ...read more.

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