• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
• Level: GCSE
• Subject: Maths
• Word count: 8927

# mayfeild statistics

Extracts from this document...

Introduction

By Nandini Murji 11G

Candidate No. 2123

Mayfield Coursework

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.

Middle

16

1.68

63

11

Lewis

James

16

1.68

56

11

Joseph

David

16

1.62

92

11

McDonald

James

Harold

16

1.62

50

11

McGuire

Frederick

16

1.67

70

11

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.

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.)

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.

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

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.

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.

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

Conclusion

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.

Box Plot for Girls - Weight

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)

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:

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.

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

# 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. ## Edexcel GCSE Statistics Coursework

Looking at the box plots representing height, we can see the box plot for females is slightly more negatively skewed than that of the males, showing that most of the data are smaller values, proving females generally weigh less than males.

1. ## freezing point depression method

A graph of temperature against time was plotted to show the freezing point for naphthalene only, naphthalene + (0.50 to 0.75g X) and naphthalene + (0.50 to 0.75g X) + (0.15 to 0.25g X). The freezing point for naphthalene we get in this experiment was 78 oC which is two degrees lower than the theoretical value which is 80 oC.

2. ## Conduct an investigation comparing height and weight from pupils in Mayfield School.

46 (x - 46)� 53 7 49 47 1 1 50 4 16 54 8 64 50 4 16 44 -2 4 38 -8 64 52 6 36 48 2 4 45 -1 1 50 4 16 44 -2 4 53 7 49 57 11 121 40 -6 36 40

1. ## Does Foot Size Increase With Height and Do Boys Have Larger Feet than Girls?

Both graphs have a strong positive correlation this shows that height is linked with foot size-the higher the data value for the height the larger the foot size value is. This justifies both of my graphs except for the anomalies that I have drawn, they show where my conclusion is incorrect as they do not correlate.

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

Heights and weights are quantitative and are continuous which means that the numbers are not I will record my results in tables which show the different heights and weights for girls and boys for each year group separately. This will then help me view those results to graph and interpret on to make conclusions on my hypotheses.

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

I am now able to plot my results in a bar graph, which will make my results clearer and easier to compare and analysis. To plot this graph I will be using the ratios of both sets of data. I will form a table below to tally the ratios into groups which will enable me to construct my graph.

2. ## Liquid chromatography is a technique used to separate components of a mixture to isolate ...

the resolution will improve only by V2 = 1.4. Increasing the retention factor only has a notable influence on resolution if k was small to start with. The separation efficiency of a column can be expressed in terms of the number of theoretical plates in the columns.

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