Mayfield. HYPOTHESIS 1: Boys at Mayfield School are Taller and Weigh more on average in comparison to females

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Mayfield School Mathematics Statistics Coursework

Introduction

I have been assigned to complete a statistical investigation around the fictitious data of Mayfield High School, which has data of a real school. I will be completing this investigate for the subject Mathematics: Statistics. By completing the task that I have been set this will help me achieve my aim which is to gain a General Certificate of Secondary Education in this very particular subject. I will be using various techniques that I have recently studied and learnt and captured to produce a successful & efficient coursework. Alternating Statistical Methods will be used throughout this assignment to prove if my hypothesis is either correct or incorrect.

Task/Situation

I have decided to investigate majorly between the relationship between the height and weight of the pupils and to tell whether or not there is any correlation between them. I will take many actions as possible in achieving pure and efficiently results to meet the needs and requirement of my assignment. To meet my particular aim I will use many statistical interpretations and methods to help me form sufficient conclusions on what I have gained and obtained from the evidence that I will be collecting for this project.

My Hypothesis

A hypothesis is the outline of the idea/ideas which I will be testing and below are the following hypothesis I have decided to investigate for this particular assignment:

o ' Boys at Mayfield School are Taller and Weigh more on average in comparison to females'

o 'Key Stage 4 Students who watch more hours of television on average have a lower IQ Level'

o ' Left Handed Students have higher IQ levels and Key Stage 2 Results in

Comparison right handed student at Mayfield High School'

I will now investigate the correlation between the hypothesis that I have decided to investigate and proceed with a full investigation.

HYPOTHESIS 1: 'Boys at Mayfield School are Taller and Weigh more on average in comparison to females'

Planning

I will need the data of Mayfield High School between the Years of 7 to 11 and this is due to the fact for a wider sampling range and sufficient and unbiased results and uses many sampling methods to make my assignment unique and unbiased. The total number of students in the school is 1183. Here is a Table that I have produced which contains the number of boys and girls in each year.

Two Way Tables

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

Year Group

Number of Boys

Number of Girls

Total

7

51

31

282

8

45

25

270

9

18

43

261

0

06

94

200

1

84

86

70

TOTAL

604

579

183

I will use Stratified Sampling to investigate my First Hypothesis. This is because it took into thought all our needs of the sampling of the data; and this methods was easily accessible and can be easily manipulated and carried and only asked for a simple understanding of the subject.

The variables for the sample are gender and age so I had to do separate samples for boys and girls and vary the amount of samples taken from each year to keep the sample unbiased and insufficient. This was done as the different year groups had different numbers of pupils and it would be unfair to take the same number of samples from each year group i.e. 5 samples out of 55 is be more than 5 samples out of 200 so stratified sampling will be helpful this is due to the fact the

number of student in each year and so there is less chance of unequal representation. I will be investigating 20 boys and Girls and Boys from each Year altogether.

I will be calculating my Stratified Sampling using the Table above now and I will need calculation proportion to stratify my data spread/range.

Stratified Sampling Calculations

I want 40 Students from the from the school total 1183.

I want 20 Boys from 604 Boys and my aim is to work out how many from each year and below is my calculation

Year 7 Boys = 151 Divided By 604 multiplied by 20 = 5

Year 8 Boys = 145 Divided by 604 multiplied by 20 = 4.8 rounded of to 5

Year 9 Boys = 118 Divided By 604 multiplied by 20 = 3.9 is rounded of to 4

Year 10 Boys = 106 Divided By 604 multiplied by 20 = 3.4 is rounded of to 3

Year 11 Boys = 84 Divided By 604 multiplied by 20 = 2.7 rounded of to 3

Note * I then applied the same methods in calculating the number of Girls for my stratified sampling and here is a table of results that I will be using for my data sampling for this particular hypothesis.

Year Group

Number of Boys

Number of girls

7

5

5

8

5

4

9

4

5

0

3

3

1

3

3

Within this process the decision of choosing which students in particular to choose from within each year was done via Random Sampling.

These was done through the process in which I used a Hat to enter all the Year Group (Boys and then Girls) separately and then I mixed and entered all the names and choose an unbiased person to draw names out of the hat and below are the results of the people chosen for this sample.

I obtained these results. These results were typed up on a excel spreadsheet. Below is the Data I have gained from my Sample. Since I have investigated the Height and Weight I will only show these particular fields in my results:

) Male Stratified Sample Results

Year Group

Surname

Forename

Height (m)

Weight (kg)

7

Austin

Steven

.54

43

7

Lloyd

Mark

.61

56

7

Mills

Robert

.63

50

7

Pearce

Stuart

.50

34

7

Thorpe

Billy

.53

40

8

Freeman

Ian

.82

64

8

Jones

Kevin

.62

49

8

McGrail

Craig

.38

35

8

Peter

Zakir

.63

41

8

Wilson

Christopher

.53

32

9

Davidson

Jimmy

.61

45

9

Jones

Jimmy

.52

46

9

Jones

Brian

.32

38

9

Rowley

Geoff

.56

53

0

Bates

Markus

.80

60

0

Edd

Michael

.68

59

0

Javidson

Carlos

.70

57

1

Fairfax

Jacob

.62

51

1

Little

James

.65

47

1

Vincent

Nigel

.8

62

2) Female Stratified Sample Results

Year Group

Surname

Forename 1

Height (m)

Weight (kg)

7

Butler

Leanne

.65

40

7

Earnshaw

Catherine

.45

41

7

Meager

Becky

.64

47

7

Miles

Amanda

.46

40

7

Richards

Abbie

.53

47

8

Burton

Prudence

.59

52

8

Campbell

Julia

.41

30

8

Kudray

Rebecca

.54

52

8

Water

Rebecca

.55

57

9

Atkins

Patience

.57

40

9

Bagnall

veronica

.49

37

9

Dixon

Mary

.49

52

9

Kelsey

Sannita

.62

46

9

Mosler

Samantha

.58

36

0

Bhatti

Hannah

.72

56

0

Durst

Freda

.75

60

0

Hall

Jane

.51

36

1

Marta

Sana

.52

45

1

Ratty

Louise

.65

59

1

Peckeleka

Chantel

.56

38

Tally and Frequency Chart

Now that I have my data I will put them into frequency/tally tables to make it easier to read and it is a useful way of representing and helps view trends within my sampling that I have produced:

) Boys Heights

BOYS

Height (cm)

Tally

Frequency

30?h<140

II

2

40?h<150

0

50?h<160

IIIIII

6

60?h<170

IIIIIIII

8

70?h<180

I

80?h<190

III

3

90?h<200

0

A Pattern I have spotted in this particular Frequency/Tally table is that nearly 75 percent of boys are of the height between 150 to 170 from my sample and this shows me that students in my sample are rather tall and a steady size or above for their age group

2) Boys Weights

BOYS

Weight (kg)

Tally

Frequency

30?w<40

IIII

4

40?w<50

IIIIIII

7

50?w<60

IIIIII

6

60?w<70

III

3

70?w<80

0

0

This Tally and Frequency table shows the boy's weight and the spread of data are large and not as compact as the height whereas the height are rather scattered and vary. This however notifies me that some of the students in my sample and tall for their age but weight are average in relationship to their height.

Girls Heights

Tally and Frequency charts are regularly used to process raw data making easier to spot irregularities and patterns.

GIRLS

Height (cm)

Tally

Frequency

30?h<140

0

40?h<150

IIIII

5

50?h<160

IIIIIIIII

9

60?h<170

IIII

4

70?h<180

II

2

80?h<190

0

This table shows me nearly 50 percent of students are between the height of 150-160 and there are not many student who excel over 180 cm tall which and there are also not many if any student with a height between 130 to 140 cm which shows me that the spread of data is compact which makes it easier to view trends and also it shows that there are not many irregularities in height in the student in my sample that I have taken.

Girls Weight

GIRLS

Weight (kg)

Tally

Frequency

30?w<40

IIIII

5

40?w<50

IIIIIIII

8

50?w<60

IIIIII

6

60?w<70

I

70?w<80

0

Comparisons of Tally & Frequency Table

I will now compare each of the tables of girls & boys height and then weight and view the differences in trends and if there are and mistakes or bias.
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Height Comparison: From the Sample I have taken I have come to find that boys grow rapidly at a later age whereas girls grow faster from an earlier age and stop at a particular age also. This is shown since I have found that 2 students are of a height between 130- 139 cm, which shows that my data may be misleading or there is a lapse in growth. Both Girls and Boys have average heights and are fairly balanced and of equal size. Although my Sample shows that boys on some occasion grow to above average height ...

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