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GCSE Maths Statistics Coursework

Extracts from this document...

Introduction

1st of February 2006 GCSE Mathematics Coursework- Data Handling Hypothesis: Children between Year 7-11 change physically and mentally as they mature. Aims: To investigate my hypothesis I have set some aims: * To investigate the height change between year groups * To observe correlation between IQ and age * To investigate changes in favourite TV genre choice Introduction: I have chosen to investigate this hypothesis for my coursework because I think it will be interesting and lead to many fascinating questions and hopefully answers. Method: To investigate my aims I intend to take a sample of the data. I will take a stratified sample of the data taking a proportion of boys and girls from every year group. To take a stratified sample I will divide the whole population of children into year group and gender e.g. Year 7 Boys. I will then take 10% of each stratum to gain fair representation of each stratum. Having taken this sample I will attempt to answer aim 1. I will group together the height data within the stratum creating a frequency table. From this, I will plot a cumulative frequency graph. After this, I will find the median, the upper and lower quartiles and create a "box and whisker" plot. I will do this to each strata, place all 5 "box and whisker" diagrams on the same page and compare them. I will use "box and whisker" diagrams as they should be able to see the jump in heights between the year groups clearly. I will also be able to asses the skew of the data. I will do this for boys and girls separately as they have their growth spurts at different times. I will take that standard deviation of the children's heights as this will allow me to see how far spread the children's heights are in relation to the mean average. From this information, I should be able to infer a judgment on some of the physical changes of children between these ages. ...read more.

Middle

All though the ranges do not necessarily reflect this observation, I can see that the inter-quartile ranges are slowly creeping up, with the age. There is one exception in between Year 8 girls and Year 9 girls however; I think this can be accounted for as they are close, Year 8 shows a large range of heights, (three standard deviations from the mean) and this may have caused the discrepancy in the data. (Outliers may have affect the median point, upper and lower quartile points on which the box and whisker is based.) Or it could simply be that Year 8 is exceptionally tall whilst Year 9 small for their age. I think the former explanation is the more plausible of the two having studied the charts and the standard deviations. In the Year 7 girls, the middle 50% - inter-quartile range, is far larger than that of the Year 10 or Year 11 girls. Year 7 has some largely differing heights within the middle 50% where as in Year 10 and 11 the heights of the middle 50% of the girls has come a lot closer. I think this is probably because the girls in Year 7 are split generally into those who have come into puberty and those who have not. Some of them will have had growth spurts where as others will have that to come. This means that the inter-quartile range will be further spread. However, when analysing the Year 10 and 11 charts the inter-quartile range is far smaller. I believe the reason for this is that the Year 10 and 11 girls have more or less, all been through the puberty growth spurts. There is still some differing individual difference nevertheless; they have largely achieved a roughly similar height. The largest growth spurt on the charts seems to be between Year 7 and Year 8 for the girls. ...read more.

Conclusion

From this, I found the spearman's rank correlation between the Year 7 girls and the Year 11 girls and the Year 7 boys and the Year 11 boys. I also plotted some pie charts using Microsoft Excel Application to show the percentage of student's choices. I did this for every stratum group. The first spearman's rank I calculated was between the boys. This showed my hat there was little to no correlation. From this, I decided to re sample the Year 7 boys' and the Year 11 boys' data as the other sample was simply too small to show anything of fairness, I used systematic sample-taking every third student. After this, the larger sample showed a strong positive correlation. I repeated this process for the girls although, I did find that the smaller sample showed an equally strong positive correlation I took the re-sample just to be sure. I think that the girls may have shown more of a correlation - even in the small sample because girls tend to develop before boys and they may have developed these TV preferences before Year 7 age group where as the boys are later with the changes which show up in my sample age. This is re-iterated by the fact that the Year 11 boys data it is far more spread than the Year 7 boys data. By looking at the frequency charts you can see that the Year 11 boy's have branched out their choices, they have less people watching cartoons and soaps and more people watching educational programs and sports. This shows that the Year 11 boy's have a wider range of interests and are more open to new things, this makes them more mature than they where in Year 7. The pie charts show this is true of both sexes. Although they chose the same top programmes for each age group, they have branched out their choices. Conclusion: In answer to my aim, I think the student's favourite choices have not differed much nonetheless; the students have become more diverse suggesting a more mature outlook. ...read more.

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