• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

mayfeild statistics

Extracts from this document...

Introduction

By Nandini Murji 11G

Candidate No. 2123

Mayfield Coursework

image00.png

Maths coursework

Aim: The aim of my investigation is to find if there is a relationship between height and weight.

Hypothesis:

‘The taller a person is, the more they weigh’.

Plan: I will start off by finding the relationship between height and weight. I have chosen to use a sample from yr11 because most students are fully mature and so they have reached their peak height therefore results obtained from this year group can be applied to society as a whole. I will use a scatter graph to find the relationships between the height and weight of both girls and boys. I will then move onto cumulative frequency and box and whisker diagrams. Once I have completed this, I will carry on by finding the variance and standard deviation.

Prediction: I predict that the taller a person, the more they would weigh. This is because there is no real difference between the proportion of fat - endomorphic, thin - ectomorphic and medium - mesomorphic people at each different height. People who are taller have a larger frame and so their bodies would carry a greater amount of flesh which would make the weight increase, so I expect that as the height increases it will be proportional to the weight as this will increase along with the height. Having done this I will try to see if there is a difference between the correlation for boys and girls. I think that it will have a positive correlation because as the height increases so will the weight.  

Introduction: I was given data based on a fictitious school called ‘Mayfield High School’. We were provided secondary data which we have to use to help us with the investigation.

...read more.

Middle

16

1.68

63

11

Lewis

James

Adam

16

1.68

56

11

Madalin

Joseph

David

16

1.62

92

11

McDonald

James

Harold

16

1.62

50

11

McGuire

Frederick

16

1.67

70

11

Nadeem

Ammad

16

1.97

84

11

Nickholas

Danny

Michael

16

1.52

38

11

Nolan

Ahmed

16

1.84

78

11

Paul

Niel

Martin

16

1.72

64

11

Perlains

Carl

Edward

16

1.76

62

11

Robinson

Luke

16

2.06

84

11

Smith

Michael

Jason

16

1.52

45

11

Spern

Jon

16

1.7

54

11

Vincent

Nigel

Barry

16

1.8

62

Mean=1.74

Mean=63

These are the final 30 results I obtained after using the ‘simple random sampling’ technique.

The two yr11 boys which are highlighted in red are outliers. So I will remove these from my data and will replace them. I will again repeat the ‘random sampling’ process.

I have worked the mean out so that it can help me find the line of best fit as it should pass through this point. I worked out the mean for both the height and weight and worked it out in the following way:

Data for boys:

Year Group

Surname

Forename 1

Forename 2

Years

Height (m)

Weight (kg)

11

Small

Peter

John

15

2

60

11

Solomon

Michael

Christopher

15

2.03

86

11

Cullen

Peter

Harry

16

1.88

75

11

Cullen

Sam

16

1.55

54

11

Cunning

Kenneth

Lloyd

16

1.51

40

11

Curtis

david

John

16

1.78

67

11

Fairfax

Jacob

James

16

1.62

51

11

Fasworth

John

16

1.79

72

11

Fisher

Carl

Scott

16

1.8

72

11

Frost

James

Jackson

16

1.85

73

11

Hawkins

Tim

16

1.62

63

11

Heath

Malcom

John

16

1.75

68

11

Hossany

Selim

Waseem

16

2

86

11

Johnson

Sean

16

1.69

65

11

Khan

Assad

16

1.68

63

11

Krane

Assad

16

1.68

63

11

Lewis

James

Adam

16

1.68

56

11

McDonald

James

Harold

16

1.62

50

11

McGuire

Frederick

16

1.67

70

11

Nadeem

Ammad

16

1.97

84

11

Nickholas

Danny

Michael

16

1.52

38

11

Nolan

Ahmed

16

1.84

78

11

Paul

Niel

Martin

16

1.72

64

11

Perlains

Carl

Edward

16

1.76

62

11

Robinson

Luke

16

2.06

84

11

Smith

Michael

Jason

16

1.52

45

11

Spern

Jon

16

1.7

54

11

Vincent

Nigel

Barry

16

1.8

62

11

Olderson

Stuart

Martin

16

1.62

48

11

Downey

Colin

Clarke

16

1.68

50

Mean=1.75

Mean=63.43

I have now changed both of the outlier values, and have replaced them with the two results which are highlighted above.

Averages

I will start off by working out the averages. The three most common ways are to work out the mean, median and mode so I will do this.

Mean

The mean is worked out by adding all the list of numbers and then dividing it by the quantity.

I have worked out the mean for each the height and weight for the boys. image03.pngimage04.png

Median

The median is the mid-value of a list of numbers, once it has been put into order. (Start with the smallest and end with the biggest.)

image54.png

image05.pngimage06.png

image07.png

image59.png

image08.pngimage09.png

image10.png

Mode

The mode is the value which occurs most often.

In this set of data the modal height is 1.62 as this is the most common height from this set of data for the boys.

Height, x

f

2

2

2.03

1

1.88

1

1.55

1

1.51

1

1.78

1

1.69

1

1.62

4

1.79

1

1.8

2

1.85

1

1.75

1

1.68

4

1.67

1

1.97

1

1.52

2

1.84

1

1.72

1

1.76

1

2.06

1

1.7

1

                                    The modal heights. I would                      expect these to lie within the inter-quartile range. image11.png

image13.png

In this set of data the modal weight is 63 as this is the most common weight from this set of data for the boys.

Weight, x

f

60

1

86

2

75

1

54

2

40

1

67

1

48

1

51

1

72

2

73

1

63

3

68

1

65

1

56

1

50

2

70

1

84

2

38

1

78

1

64

1

62

2

45

1

60

1

image14.png

                                       The modal weight. – I would expect this to lie within the inter-quartile range.

The median and mode are not influenced by outliers, but the mean is influenced by outliers. This means that the value of the mean may not be accurate as there may be outliers in my set of results.  

Data for girls:

Year Group

Surname

Forename 1

Forename 2

Years

Height (m)

Weight (kg)

11

Ali

Amera

15

1.62

56

11

BrownIsabella

15

1.65

66

11

Dawson

Jane

Samantha

15

1.70

50

11

Alexander

Claire

16

1.60

54

11

Barlow

Hanah

Mary

16

1.63

44

11

Berry

Shelly

Laura

16

1.73

64

11

Briggs

Sarah

Louise

16

1.63

48

11

Chong

Sabrina

Kamala

16

1.61

54

11

Godfrey

Amanda

Eve

16

1.58

54

11

Green

Teresa

16

1.37

30

11

Hall Julie

16

1.63

52

11

Heap

Louise

Stephanie

16

1.80

42

11

Hall Julie

16

1.63

52

11

Hayson

Louise

Jade

16

1.57

48

11

Heap

Louise

Stephanie

16

1.80

42

11

Hunter

Ingrid

16

1.52

44

11

Iilyas

Ameri

16

1.62

48

11

Jackson

Debi

16

1.68

50

11

Kaleem

Humaira

16

1.69

54

11

Kelly

Freda

Jane

16

1.60

45

11

Kerry

Leilah

Nina

16

1.70

63

11

Margeus

Nichola

Paula

16

1.61

45

11

McCarthy

Farrah

16

1.59

42

11

McMorrison

Victoria

Catherine

16

1.65

52

11

Mitchell

Nikayah

Serenah

16

1.73

48

11

Murphy

Stacey

Ann

16

1.62

54

11

Peckeleka

Chantel

Norma

16

1.56

38

11

Peterson

Louise

Gemma

16

1.65

54

11

Skeely

Jenifer

16

1.60

66

11

Thompson

Kamara

Paula

16

1.71

42

Mean=1.64

Mean=50

These are the final 30 results for the girls I obtained after using the ‘simple random sampling’ technique.

I have worked the mean out so that it can help me find the line of best fit. I worked out the mean for both the height and weight and worked it out in the following way:

Averages

I will now start working out the averages for the girls. The three most common ways are to work out the mean, median and mode so I will do this.

Mean

The mean is worked out by adding all the list of numbers and then dividing it by the quantity.

I have worked out the mean for each the height and weight for the girls.

image16.pngimage15.png

Median

The median is the mid-value of a list of numbers, once it has been put into order. (Start with the smallest and end with the biggest.)

The median height for this set of data is 1.63.

The median weight for this set of data is 50.

I will later compare these calculated values with the one I shall obtain from my cumulative frequency graph.

image65.png

image17.png

image18.png

Mode

The mode is the value which occurs most often.

In this set of data the modal height is 1.63 as this is the most common height from this set of data

...read more.

Conclusion

image61.png

This is the frequency table which shows the frequency for the height for the girls. I will use this to make my cumulative frequency graph.

The cumulative frequency curve below is the cumulative frequency graph for the weight of both girls and boys.

image40.png

image42.png

Box Plot for Girls - Weight

image62.png

This box plot shows that the median is 50. The lower quartile 44 and the upper quartile is 54. The inter-quartile range is 10. The minimum value is 30 and the maximum value is 66.

Box Plot for Boys – Weight (Kg)

image63.png

This box plot shows that the median is 63.7. The lower quartile is 51 and the upper quartile is 70. The inter quartile range is 19. The minimum value is 5.5, the maximum value is 92.5. This is positively skewed because the data is bunched up on the left side of the centre.

Conclusion:

I found that my hypothesis was correct and in most cases, the taller the person the more they weighed. Although, there were outliers which could be there for various reasons. I found that the boys weighed more than the girls did as a minimum weight. And the maximum weight for both was

BMI – Body Mass Index

Body Mass Index (BMI) is the number, derived by using height and weight measurements, that gives a general indication if weight falls within a healthy range.

The formula for BMI is: image64.png

In recent events we found that the models in Madrid were rejected in some of the fashions shows because their BMI was low. Although because their BMI was too low it didn’t mean that they starved themselves, it could have meant that they had a high metabolism and burn up their food very quickly.  

I will start by calculating the BMI for the boys data:

Height, x

Weight, y

BMI

2

60

15

2.03

86

20.86923

1.88

75

21.22001

1.55

54

22.47659

1.51

40

17.54309

1.78

67

21.14632

1.62

51

19.43301

1.79

72

22.47121

1.8

72

22.22222

1.85

73

21.32944

1.62

63

24.00549

1.75

68

22.20408

2

86

21.5

1.69

65

22.75831

1.68

63

22.32143

1.68

63

22.32143

1.68

56

19.84127

1.62

50

19.05197

1.67

70

25.0995

1.97

84

21.64446

1.52

38

16.44737

1.84

78

23.03875

1.72

64

21.63332

1.76

62

20.0155

2.06

84

19.79451

1.52

45

19.47715

1.7

54

18.68512

1.8

62

19.1358

1.62

48

18.28989

1.68

50

17.71542

Now I will calculate the BMI for the girls data:

Height, x

Weight, y

BMI

1.62

56

21.3382

1.65

66

24.2424

1.70

50

17.301

1.60

54

21.0938

1.63

44

16.5607

1.73

64

21.3839

1.63

48

18.0662

1.61

54

20.8325

1.58

54

21.6311

1.37

30

15.9838

1.63

52

19.5717

1.80

42

12.963

1.63

52

19.5717

1.57

48

19.4734

1.80

42

12.963

1.52

44

19.0443

1.62

48

18.2899

1.68

50

17.7154

1.69

54

18.9069

1.60

45

17.5781

1.70

63

21.7993

1.61

45

17.3604

1.59

42

16.6133

1.65

52

19.1001

1.73

48

16.038

1.62

54

20.5761

1.56

38

15.6147

1.65

54

19.8347

1.60

66

25.7813

1.71

42

14.3634

Conclusion:

The BMI figures show that most people are healthy.

...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.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

  1. mayfield high statistics coursework

    Boys from my Stratified Sample also on average are 6 cm taller than Girls. Mode of Girls and Boys Weight The arithmetic mean of a group of numbers is found by dividing their sum by the number of members in the group; e.g., the sum of the seven numbers 4,

  2. Mayfield High Statistics Coursework

    in addition to measure of central tendency (such as mean, median or mode). For example, the following two data sets are significantly different in nature and yet have the same mean, median and rage. Some sort of numerical measure which distinguishes between them would be useful.

  1. Edexcel GCSE Statistics Coursework

    A thin box relative to the whiskers indicates that a very high number of cases are contained within a very small segment of the sample indicating a distribution with a thinner peak whereas a wider box is indicative of a wider peak and so, the wider the box, the more U-shaped the distribution becomes.

  2. Maths Statistics Coursework - relationship between the weight and height

    I am planning to do the calculations in a variety of ways. I will be calculating the averages by using a calculator using the statistical functions on it. I will be using Microsoft Excel software to help me to calculate the product-moment correlation coefficient (PMCC)

  1. Maths Statistics Coursework

    more mature at a younger and therefore because of their majority they would work harder than their male counterparts who are less mature. By year 11 the boys should have matured enough to match their female counterpart's work ethic and his would help them to get better grades catching up and in some situations passing the girls grades and IQs.

  2. Investigation on the shape and size of limpets on a sheltered rocky shore called ...

    the limpets are still able to survive, as this zone get covered in water for about 80% of the year. So these height/base ratios found at 3m are most suitable for the limpets as they live in such harsh conditions and so these low ratios will make the limpets more

  1. In this coursework I want to find out what the average height, weight, and ...

    Are Year 11 Pupils Square (Male & Female Data) I will now want to try and find out if Year 11 Males are squarer than Year 11 Females. Here are my two scatter diagrams for Male and Female data; From these two scatter diagrams I can see clearly that

  2. GCSE maths statistics coursework

    was larger for boys than that of the girls as both went up to 1.9m although the frequency density between 1.7m to 1.9m was larger than the frequency density of the girls. I will now do frequency polygons of the girls and boys weights.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work