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  • Level: GCSE
  • Subject: Maths
  • Word count: 1918

The relationship between height and weight amongst different ages and genders

Extracts from this document...

Introduction

        Statistics Coursework        

The relationship between height and weight amongst different ages and genders

PLAN

Introduction

I have been given a set of data about different pupils attending a school called Mayfield High School. The data which I have extracted from this are the pupils’ year group, age, height, weight and gender. Therefore, I have decided to compare the changes in the heights and weights of the pupils and how they are different amongst the different year groups and genders.

Hypothesis

I think that as the year group increases, the heights and the weights will increase. However, I think that the heights and weights will increase; but at a decreasing rate. I think that this will happen from my own experience since year 7; I have increased in height and weight, but have not increased them at an increasing rate.

Sampling

The data which I have been given is very large, so I need to decrease the amount of data so it is easier to work with and analyse. Therefore, I will sample the data with a stratified sample, which means I will pick a fraction of the data but the new data will still represent the overall data. For example, if 51% of the pupils are male, then my sample will still have 51% male pupils.

...read more.

Middle

Planning the analysis

To try to prove my hypothesis, I will take the mean and median of the data of each year, and work out what the percentage difference is from year to year. If my hypothesis is right, then the heights will increase faster than the weights.

RESULTS

Box plot of heights

image00.png

Results table of heights

HEIGHTS

Year 7

Year 8

Year 9

Year 10

Year 11

Mean

1.55

1.63

1.65

1.67

1.68

Range

0.3

0.31

0.36

0.40

0.56

Lower quartile

1.50

1.56

1.58

1.62

1.60

Median

1.56

1.65

1.62

1.67

1.67

Upper quartile

1.60

1.70

1.76

1.77

1.72

IQR

0.10

0.15

0.18

0.14

0.12

...read more.

Conclusion

Sampling

The data which I will be comparing will be the same as the data I used for my previous investigation. Therefore, the data I will use should represent the data for the whole school.

Calculations

Gradient of the lines: This is important because it will allow me to see how the weight increases with height and by how much. It will also prove or disprove my hypothesis, so if for example the gradient for boys is larger than girls, then I will know that my hypothesis is right, because it will prove that the weights for boys increases by a larger amount than for girls.

Diagrams and tables

I will use a scatter diagram to prove my hypothesis. This will help me because I can see the equation of each line that I make. Therefore, I can see the equation for the boys and the girls. From this, I will be able to calculate the gradient, and so prove or disprove my hypothesis.

RESULTS

Scatter diagram

image04.png

Data of lines:

Boys: y=51.84x-30.08. Gradient = 51.84

Girls: y=23.05x+11.93. Gradient = 23.05

ANALYSIS

The scatter diagram shows that with the boys, the weight increases by a greater amount with the weight than with the girls. Therefore, this proves my hypothesis.

...read more.

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