Statistics Coursework Essays

Statistics Coursework Essays Statistics Coursework Essay Statistics Coursework Essay I have been asked to examine the students attendance figures from all year groups (7, 8, 9, 10 and 11) at Hamilton Community College. I will be investigating whether the age of the students affects their attendance figures at school and does it affect their learning and exam results as well? To start my research, I was given the attendance figures by the school for all of the year groups for the 2003 2004 academic years. I will then start to process data (attendance figures) firstly by reducing the amount of data that I will have to process using the method of stratified sampling. By using stratified sampling I will then only use a fair amount of data according to the percentage that Im comfortable with. I will only be using 20% of the attendance figures from each year. A scientific calculator is used, to randomly select attendance figures that I am going to use, so that the new set of statistics isnt bias and isnt affected by my conscious decision. Using the new set of data, I will collate the data in frequency tables (to display all of the frequency distributions), in order to enable easy interpretation and analysis. Secondly, after collating the data, I will then display the new set of data in forms of graphs/diagrams and charts so that it will be easier for me to compare and study the figures. From these graphs/diagrams and charts, I will calculate the central tendency for all the year groups (mean, median) and also the dispersion of each year group by calculating the quartiles (upper quartile, lower quartile and interquartile range) which will also ensures that the figures that I am going to process and compare are only the true average (middle 50% of the data). It is vital for me to choose the most appropriate graphs/diagrams or charts to display the datas properties effectively and clearly. Graphs like the normal distribution curves are ever so important in these type of investigation especially because the graph itself summarise so many vital information such as the Thirdly, I will then analyse all of the results that I will get from the calculations and evaluate it against my hypothesis. I will analyse all of the data in a more depth by doing standard deviation and Spearmans rank correlation coefficient that will allow me to compare and analyse the data properties using different methods. Finally, I will then come to a conclusion stating whether the age does or does not affect the attendance of the students and their learning at school. Hypothesis Does the age of the students affect their attendance at school? There is a probability that there is a small relationship between the age of the students and their attendance figures at school or there is no relationship at all. However, the students appreciation of the importance of their attendance figures does and this is why (in my opinion) the attendance figures vary between students. Nevertheless, the students that are within their exam years should have a much higher attendance percentage than those who dont. In my opinion, age does not affect the attendance of the students at all. I think the attendance figures of the students at Hamilton totally depends on the students environment and maturity in terms of their understanding of the importance of their attendance figures at school (e.g. for future reference when their career year approaches). However, even though it seems like the Year 11 GCSE students tend to come to school much more often or supposed to attend school everyday than the Year 7s, to me, this doesnt have any relations with age at all. Just because the student is a Year 7 pupil, that doesnt mean that their attendance figures are going to be really low. This also applies for the GCSE students (Year 10s and 11s); just because the student is taking their GCSE it doesnt mean that their attendance is going to be a full 100% (even though it should be like that). A Year 7 pupil could have a 100% attendance figure just like a Year 11 student and it doesnt have to relate to age at a ll. A 6, 10, 12 and even 15-year-old students can still have a stunning 100% attendance figures at school just by having that one important reason of why they have to come to school everyday (and again it might not have anything to do with age at all). So, I do not believe that the age of the students affect the attendance at school. Does attendance affect the students learning and their exam results? There is a relationship between the attendance of the students and their exams results. Students who comes to school often or everyday, to learn, tend to improve and have much better exam results than those who dont. I believe that the attendance of a student does affect their exam results. For students who come to school everyday learns more than the students who dont attend regularly. Therefore, more education equals better exam results. But, there are some students, who do not come to school as often as they should but still get good results (naturally clever as people would say it). This is true and I agree. However, I think these extraordinary students must have another form or way of learning when not at school (the student might be an independent learner for example). But for those who are not an independent learner and still get wonderful exam results, they might concentrate hard in lessons when they are actually in school and absorbs everything that they learn. So, basically overall, I think the attendance of the students does affect their learning and exams results. Plan 1. In order for me to investigate this problem, I was given a secondary type of data of the attendance of all the students in Hamilton Community College in the 2003 2004 academic years from Year 7s to Year 11s. It would be unreasonable and difficult for me to use all of the data given, as it will consume a lot of time during the calculation process. Because of this Ive decided to use the stratified sampling method to handle the vast amount of data. This way, it does not only reduce the amount of time for me to process the data, it also reduces its quantity. The attendance figures of all of the students will be divided according to the year groups they belong to in ascending order (0% 100%). I will then label them from 1 to how many attendance figures there are in the year group (1, 2, 3267). By using a scientific calculator, I will use the RANDOM button to randomly select 20% of the total attendance figures in the particular year. This way, the new set of data will not only be much smaller, but also ensures that I have a fair proportion of responses from each year and it is not bias as it is done without my conscious decision. 2. The new stratified data will then be investigated, compared and analysed with each other to see whether it matches with my hypothesis. Since that the data is a grouped, continuous data, below are the graphs/diagrams and charts that I will be using to display the data clearly: 2.1 Cumulative frequency polygons A cumulative frequency polygon shows the trend of growth of continuous data. It is also useful for estimating how much more or less there is than a certain amount. So, I will be able to estimate the averages much easier using these graphs rather than using tables. By using cumulative frequency polygons, I can also calculate the quartiles of the data, which will not only measure the spread of the data but also display the central 50% of the data (excluding the highest and lowest value interquartile range). This could be shown much evidently by using the box and whiskers diagram. 2.2 Box and whisker diagram The box and whisker diagram will be used to stress the quartiles and also to show its (shape) distribution whether it has a symmetrical distribution, negative skew or positive skew. It also shows the median of the data. Box and whiskers diagram can be easily compared with each other to see which year group have a stronger (higher) percentage of attendance during the academic year. 2.3 Histograms I am going to use histograms instead of bar charts is because the data Im using is a continuous grouped data. Histogram uses the area of the bars to represent the frequencies rather than the heights like normal bar charts. It may have equal or unequal intervals. A histogram with equal intervals is a frequency diagram (only the height of the bars vary), however, a histogram with unequal intervals, the area of each bar is proportional to the frequency of each class and the height of the bars are based on the frequency density. By using histograms, I am then able to see the shape of the distribution, whether it has a symmetrical distribution and positive or negative skew. 2.4 Standard deviation Standard deviation is the square root of a variance. Variance is a measure of spread that uses all of the data. By doing the standard deviation I am then able to see the Normal distribution for each year and also compare them with each other and see much more clearly which year group have a higher attendance figure. 2.5 Spearmans rank correlation coefficient The spearmans rank correlation coefficient is going to be used for the Year 9 attendance and their SATs results to see how they correlate with each other. This will prove whether attendance have an effect on their exam results or people who get good results are just naturally clever. 2.6 Normal distribution Normal distribution is a family of distributions that have the same general shape. They are symmetric with scores more concentrated in the middle than in the tails. Normal distributions are sometimes described as bell shaped. 2.7 Scatter diagrams The relationship between two variables can be shown through scatter diagrams. By using scatter diagrams, I am able to see the correlation clearly and state whether the variables have any sort of relationship together. However, this can be looked at in depth with spearmans rank correlation coefficient. 3. The reason of why I am using ever so many graphs/diagrams and charts is because I believe that you cannot display all of the information you want to display by using a single graph in this investigation. Further more, the more (appropriate) graphs/diagrams and charts I do, the more information Ill receive on the attendance of each year group. Also, I will be able to compare the results in a much better way and give a more specific answer towards the research. 4. Using all of these diagrams I will then compare all of the students attendance for each year. Then I will also analyse all of these graphs and diagrams and actually come to a conclusion that tells me all the information I need (e.g. which year group have the best attendance figures) for this investigation. 5. With this final conclusion I will compare it against my hypothesis and evaluate it to see whether it has any connections towards my hypotheses I worked out earlier. Finally, I will then state whether or not the final statement has anything to do with the hypotheses. Below is the secondary data Ive received of the attendance of the school according to each year.