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.

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:

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.

                                    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.

                                       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:

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

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:

Now I will calculate the BMI for the girls data:

Conclusion:

The BMI figures show that most people are healthy.