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# maths coursework sampling

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Introduction

GCSE Coursework :

INTRODUCTION

The data which I have to use in this coursework was collected from 100        Year 7 (50 boys, 50 girls) and from 100 Year 10 (50 girls , 50 boys). All the pupils were asked  to estimate measurements on the data collection sheet given to them.

1. the lengths of two lines
2. the sizes of two angles
3. the area of two shapes

Aim:

Statistics is a very important tool in analysing data and it is the science of summarising and analysing data that are subject to random variation.  The main purpose of this investigation is to test 3 hypothesis by analysing  the data .

.

Plan:

Sampling

Usually it is not possible to study the entire population in which one is interested. It is therefore necessary to consider a sample and to relate its characteristics to the total population. To begin my task I need a sizeable and manageable set of data to use and test. The data provided comprises of 200 pupils. I wish to sample this data so that samples could be analysed statistically to see the relationship between two selected variables for the entire data collected from upper and middle sets of year 7 and year 10.

Although there are various ways of sampling the data, but I will stick to three main types of sampling which would be random, stratified and systematic. I shall also make sure that any bias is avoided during this sampling technique

Middle

I have accepted this hypothesis because I have produced a scatter graph for the above data and there is positive correlation between the estimates of  length A and  estimates of length B Year 7 pupils.

 Numbers Length A Length B 1 30 62 2 35 80 3 30 40 4 40 90 5 50 140 6 30.5 90.5 7 3.5 6.5 8 1.5 25 9 13 253 10 3 7.5 11 25 95 12 25 60 13 35 110 14 25 65 15 25 100 16 34 95 17 50 120 18 13 28 19 35 100 20 30 80 21 30 70 22 30 60 23 35 65 24 40 90 25 40 100 26 35 72 27 40 70 28 50 100 29 34 100 30 32 63

Hypothesis 2

The distributions of estimates for angle C

Conclusion

Overall, two hypothesis’ tell me that year 10 are better at estimating but hypothesis 1 may overrule this statement.

Hypothesis 3

By looking at frequency polygon, I would  say that my hypothesis is right. The distributions of estimates of Length A for Year 7 are approximately the same as they are for Year 10.  The standard deviation also clearly shows that Year 10 estimates were less distributed than Year 7. The standard deviation shows that Year 7 estimate range was 20.419 degrees and Year 10s was 6.892 degrees. This clearly shows that the year 7 standard deviation was much more hence the estimates were much more distributed. Year 7s mean was also a lot closer to the correct answer than Year 10s. Year 7s mean was 32.27 while Year 10s was 26.22. The correct answer was 15 degrees and 26.22 is closest. This shows that age does matter. Year 10 results were generally close to the correct answer and this suggests my hypothesis wrong. This is probably because Year 7 do not have the required skills at year 7 because they year 10 students are more aware of estimation and have a higher range of mathematical skills than year 7.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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