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# 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

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

Black

9

94

48

Ashcroft

Wayne

Paul

Brown

23

108

37

Mevine

Gary

Clark

Black

15

104

50

Khan

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

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

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

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

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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