- Level: AS and A Level
- Subject: Maths
- Word count: 5573
The average pupil.
Extracts from this document...
Introduction
GCSE Maths Coursework
The average pupil
The aim of this study is to find the statistics for the average school pupil. This will be achieved by looking at the results of a survey carried out at Jordan Hill comprehensive.
Hypotheses:
How the education system has changed in its efficiency, over four years.
The weight of a pupil will increase with the amount of television watched per week.
The hair colour of a pupil will affect their IQ.
How I will achieve this?
This will be achieved by using samples of the given material. Specifically a sample of 50 people will be used for the first hypothesis, and then a sample of 30 will be used for the next two hypotheses, as to not be too time consuming. I will be using a stratified sample for the first hypothesis, and then a random sample from that point forward.
Why am I using Stratified and Random sampling to acquire my sample?
From studying the data sheets I have decided to use a stratified sample. I have chosen this method because it would appear to be the most efficient method of sampling in order to tackle this amount of data, and I feel that the sample is plenty large enough for the results to be significant.
I have also chosen a random sample because it cannot become bias, if some strata are larger than others. This is also because gender, or age will not affect the two last hypotheses. It will also provide me with something to compare the sampling methods with in the conclusion, and give a broader sample of the entire school, as opposed to just year 7’s, or year 11’s. Both are perfectly viable methods, as opposed to systematic or attribute sampling.
How I will display my data?
Middle
48
Read
Louise
Emma
Honey/blonde
14
79
48
Martin
Todd
Black
30
88
52
Jags
Phil
Fair
12
102
68
Murphy
Stacey
Ann
Brown
10
106
54
Bodman
Mikeal
Christopher
Brown
8
72
38
Jervis
Peter
William
Black
14
103
40
Justice
Tony
Philip
Black
24
98
60
Victoria
Carol
April
Black
16
88
55
Andrews
John
Blonde
20
101
45
Bigglesworth
Wayne
Gregory
Brown
14
91
66
Cassel
Diane
Brown
5
11
46
Ingleton
Elizabeth
Sarah
Brown
20
114
37
Friend
Aaron Carl
Blonde
20
102
60
Hunt
Gareth
Barry
Brown
3
102
62
Bhatti
Sadia
Black
9
94
48
Ashcroft
Wayne
Paul
Brown
23
108
37
Mevine
Gary
Clark
Black
15
104
50
Khan
Adila
Black
14
120
48
Sayers
Ben
Blonde
10
101
40
Black
Mia
Sarah
Brown
14
103
57
Thompson
Kamara
Paula
Brown
6
89
42
Hardy
Rhys
Black
14
90
45
Madden
Ben
Blonde
10
106
47
Vegeta
Goku
Krillain
Black
65
109
35
McAther
Dougie
David
Blue
170
101
60
Large
Stephen
Daniel
Brown
12
103
26
Hypothesis 2: The weight of a pupil will increase with the amount of television watched per week.
This hypothesis uses two sets of data (weight and amount of television watched per week) that can be grouped. This will allow me to accurately compare the two sets of data, and I should therefore be without any problems. After I have compared the sets of data I have ascertained, I should be able to accurately find out whether, or not there is any correlation between the two sets of data.
I will start by comparing histograms for both sets of data;
Initially, the table for weight
Weight (kg) | Frequency | Class width | Frequency density |
0<weight<30 | 1 | 30 | 0.3 |
30<weight<40 | 6 | 10 | 0.6 |
40<weight<50 | 11 | 10 | 1.1 |
50<weight<60 | 8 | 10 | 0.8 |
60<weight<70 | 4 | 10 | 0.4 |
As you can see from the graph I have drawn, there is a large amount of pupils weighing 30kg, or less. However, there is a large increase in the amount of pupils weighing more than this as I move up the graph. If my hypothesis is correct then this will be the group of pupils who watch the most television per week.
Now I will draw the frequency density table for the number of hours of television watched per week.
Tele hours | Frequency | Class width | Frequency density |
0<TV<10 | 9 | 10 | 0.9 |
10<TV<20 | 16 | 10 | 1.6 |
20<TV<30 | 3 | 10 | 0.3 |
30<TV<60 | 0 | 30 | 0 |
60<TV<70 | 1 | 10 | 0.1 |
70<TV<170 | 1 | 100 | 0.01 |
The graph is quite disappointing because, of the last figure it has, misshapen the scale somewhat, and produced, an almost useless graph, however I still realised that the histogram appears to have a large number of pupils who watch less than 30 hours of television per week. This graph has no correlation with the graph for weight and is therefore quite worrying, as there seems to be no connection between the amount of television watched by the students and their weight. Before I come to a conclusion however, I must study my results in more detail. Next, I will be using a cumulative frequency graph to look at my results in a different light, and be able to draw a box plot (without using excel).
Weight (kg) | Frequency | Cumulative frequency |
20<weight<30 | 1 | 1 |
30<weight<40 | 6 | 7 |
40<weight<50 | 11 | 18 |
50<weight<60 | 8 | 26 |
60<weight<70 | 4 | 30 |
Conclusion
Describe an average school pupil
Using the results I have acquired from my hypothesis, I am able to state that the average school pupil should have:
Brown hair,
An I.Q of between 100 and 110,
And it was clear to see that the education system has significantly decreased in efficiency in regards to teacher/pupil ability over four years.
These results cannot be looked upon as definite however, as my sample (displayed just before the start of hypothesis 2) was not big enough to examine the entire population. To do this I would have needed a sample of at least 300 students, and therefore an awful lot of time.
I found that when I changed to use random sampling as opposed to stratified sampling, the whole process became much easier, with no time wasted working out the correct proportions to make my particular accurate in relation to the raw data. The random sampling was easier, just to create a random sample of students and use them, and it really did eliminate any bias strata, however I am glad that I did use stratified sampling for one of my sample because it has me an insight of using it, and also has given me something to compare the random sampling against.
If I were to do this again, then I would examine my hypotheses in greater detail, as I would group the colours in my statistics in the order of the spectrum. This would allow further investigation and therefore a more in-depth comparison.
My use of cumulative frequency graphs really helped as well, as these allowed me to make comparisons between my data such as finding the median, using box plots to discover the distribution and allowing me to discover the IQR for the data through the usage of quartiles.
Most of my credit has to go to Excel though, as it was most useful during all of my tabulated and graphical representations, along with the calculations I needed.
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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