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  • Level: GCSE
  • Subject: Maths
  • Word count: 5765

Mayfield High Statistics Coursework

Extracts from this document...

Introduction

Mohammed Israr 10x1

Mayfield High Statistics Coursework

Introduction

I am going to complete a statistical investigation around the fictitious data of Mayfield high school, which has data that would represent a real school. I will be using various techniques that I have recently learnt, studied and captured to produce a successful & efficient piece of coursework.

Mayfield high is a fictitious school that consists of 1183 male and female students in years 7 to 11. The data given to me on these students comprises of height, weight, eye colour, favourite TV program, hair colour, eye colour, gender and favourite type of music etc.

Data

Data is made up of a collection of variables. Each variable can be described, numbered and measured.

  • Data that can only be described in words is qualitative. Such data is organised into categories, such as make of car, colour of hair, etc        .
  • Data which is given numerical values, such as shoe size or height, is quantitative. This type of data can be sorted into two categories:                                                                      - Discrete data can only take certain values, usually whole number, but may include fractions (e.g. shoe sizes).                                                                                                                         – Continuous data can take any value within a range and is measurable (e.g. height, weight, temperature, etc).

For my studies I will use quantitative data, this usually involves more complex graphs and studies. Quantitative data is usually grouped grouping data can be better then raw data as I can produce better visual graphs such as histograms, cumulative frequency graphs and frequency polygons.

One line of enquiry I have chosen to research is about height and weight. I have chosen these as I believe that pupil’s height and weight is affected by their age and gender especially as there are teenagers. This will help me create a hypothesis

...read more.

Middle

100

3

8

Male

103

4

8

Male

103

2

8

Male

104

3

8

Male

105

5

8

Male

107

5

8

Male

110

5

8

Male

117

5

8

Male

126

6

8

Male

127

6

9

Female

88

3

9

Female

88

3

9

Female

91

4

9

Female

93

3

9

Female

98

4

9

Female

98

4

9

Female

101

4

9

Female

101

4

9

Female

102

4

9

Female

103

4

9

Female

107

5

9

Female

121

5

9

Male

90

3

9

Male

92

3

9

Male

96

4

9

Male

102

4

9

Male

104

4

9

Male

107

5

9

Male

110

5

9

Male

112

5

9

Male

114

5

9

Male

115

5

10

Female

92

3

10

Female

100

4

10

Female

101

4

10

Female

104

4

10

Female

113

5

10

Female

116

5

10

Female

116

5

10

Male

74

2

10

Male

78

3

10

Male

88

3

10

Male

100

4

10

Male

102

4

10

Male

104

4

10

Male

109

5

10

Male

110

5

10

Male

112

4

11

Female

92

4

11

Female

97

3

11

Female

100

4

11

Female

101

4

11

Female

103

5

11

Female

108

5

11

Female

120

5

11

Male

89

4

11

Male

90

3

11

Male

99

4

11

Male

101

3

11

Male

106

4

11

Male

110

5

11

Male

127

6

image13.png

Hypothesis 2 - Boys are taller and weigh more on average in comparison to girls

Planning

I have already randomized and eliminated bias from my results using randomisation methods. Therefore I will keep the same pupils that I had chosen in my last hypothesis.

However I will still be using stratified sampling as I need a fair representation of boys and girls. Here is a table I have produced which contains the number of boys and girls in each year.

The table below is a two way table due to the fact that there are two variables shown at the same and helps view results and data conclusively.

Year Group

Boys

Girls

Total

Year 7

151

131

282

Year 8

145

125

270

Year 9

118

143

261

Year 10

106

94

200

Year 11

84

86

170

TOTAL

604

579

1183

I will use stratified sampling to investigate my second hypothesis. This is because it takes into thought all our needs of the sampling of the data; and this method is accessible and can be easily manipulated.

The variable for the sample is gender so I will do separate samples for boys and girls and vary the amount of samples from each year group to keep the sample unbiased. This is done as different year groups had different amount of pupils so it would be unfair to take the same number of samples from each year group i.e. 5 samples out of 55 is not a fair representation of 5 samples out of 200 so stratified sampling will be helpful as it will eliminate this factor.

I will be calculating my stratified sampling by using the table below:

males

females

year 7

151/603 x 50=12

131/578 x 50=11

year 8

145/603 x 50=12

125/578 x 50=11

year 9

118/603 x 50=10

143/578 x 50=12

year 10

106/603 x 50=9

94/578 x 50=8

year 11

84/603 x 50=7

86/578 x 50=8

Males

Year Group

Height (m)

Weight (kg)

7

1.62

48

7

1.62

49

7

1.52

54

7

1.47

41

7

1.61

63

7

1.60

44

7

1.57

48

7

1.55

53

7

1.73

47

7

1.62

48

7

1.54

48

7

1.50

41

8

1.72

57

8

1.25

61

8

1.52

45

8

1.32

35

8

1.50

45

8

1.70

49

8

1.68

51

8

1.72

51

8

1.48

26

8

1.59

41

8

1.54

37

8

1.67

52

9

1.75

52

9

1.58

50

9

1.52

46

9

1.73

52

9

1.50

70

9

1.50

39

9

1.71

60

9

1.55

67

9

1.60

68

9

1.74

57

10

1.73

57

10

1.80

40

10

1.67

60

10

1.55

57

10

1.65

55

10

1.74

80

10

1.57

54

10

1.73

50

10

1.60

47

11

1.73

60

11

1.64

60

11

1.61

47

11

1.84

78

11

1.57

54

11

1.61

42

11

1.97

84

...read more.

Conclusion

Evaluation

I believe that the results I analyzed from my sample are not a fair representation of my sample because I believe that as there were too many factors involved in randomizing, sorting and creating graphs etc that my results may have been incorrect or biased in some way or the other.

In my hypothesis I believe that there were a few limitations that if I believe I exceeded I would have more efficient, accurate and reliable results. Such as if I sampled more than 100 students my results would have been more reliable. I also believe that if I analysed my data more I would have more accurate results using methods such as correlation coefficient and spearman rank correlation.

When I was undertaking this hypothesis I faced a few problems which I believe could have been avoided. Firstly I believe that I could have organized my data better so it could have been analysed easily giving me better unbiased results. Such as putting my sampled data into order such as year group, gender, height and weight this would have been more efficient and would have saved a lot of time. Secondly I believe that I did not use my time effectively with this hypothesis because the articles I needed to spend less time on I spent more time on them and the articles I should’ve spent more time on I spent less time on. If I was to do this hypothesis again I would use my time more efficiently.

...read more.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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