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• Level: GCSE
• Subject: Maths
• Word count: 2378

Investigating the relationship between height and weight for the pupils in a secondary school.

Extracts from this document...

Introduction

AS Level Statistics Project

Investigating the relationship between height and weight for the pupils in a secondary school

Introduction

Primary Data by Direct Observation

Secondary Data

Hypotheses

1. Distribution

2. Comparative

Methods

Data Collection

Choosing the Data

Stratified Sampling

Randomised Selection

Analysis and Interpretation of Data

Data Summaries

Box and Whisker Diagrams

Stem and leaf and Frequency Table (Boys Height)

Stem and leaf and Frequency Table (Girls Height)

Stem and leaf and Frequency Table (Boys Weight)

Stem and leaf and Frequency Table (Girls Weight)

Standard deviation and confidence intervals

Comparing heights against Weight for Boys

Correlation Analysis

Comparing heights against Weight for Girls

Correlation Analysis

Conclusions

Evaluation

Appendix 1 – The data

Introduction

For this investigation, I am going to use data on secondary school pupils to find the distribution of the data and also to look for any meaningful relationships between the heights and weights of the students.

When I was looking at the various things that I could study, one of the factors that I looked at was data collection.

The amount of data was large, spanning across different year groups.  I could have looked at the variation of weight and height with age and with gender, but this would have made the project too long and time-consuming.

Middle

35

40

45

50

55

60

65

70

75

80

85

 35 40 45 50 55 60 65 70 75 80 85

A comparison of the Box Plots for Boys and Girls’ weight indicates that whilst there is a greater spread amongst the girls, the distributions are more comparable than with the heights.

Stem and leaf and Frequency Table (Boys Height)

 Stem Leaf Range Midpoint Frequency 1.3 5 6 1.3 ≤ H< 1.4 1.35 2 1.4 5 9 1.4 ≤ H< 1.5 1.45 2 1.5 0 0 0 1 2 3 3 5 6 7 7 7 8 9 9 9 9 9 1.5 ≤ H< 1.6 1.55 18 1.6 0 0 0 1 1 2 2 2 2 2 2 3 4 4 5 5 7 9 1.6 ≤ H< 1.7 1.65 18 1.7 0 1 5 1.7 ≤ H< 1.8 1.75 3 1.8 0 1.8 ≤ H< 1.9 1.85 1

This distribution can be seen more easily by drawing a graph:

From the look of this graph, it can be assumed that the distribution of boys’ heights is ‘normal’.

Stem and leaf and Frequency Table (Girls Height)

 Stem Leaf Range Midpoint Frequency 1.3 - 1.3 ≤ H< 1.4 1.35 0 1.4 6 7 1.4 ≤ H< 1.5 1.45 2 1.5 0 2 2 3 4 4 4 5 5 5 6 8 1.5 ≤ H< 1.6 1.55 12 1.6 0 0 1 1 2 5 5 6 6 7 7 1.6 ≤ H< 1.7 1.65 11 1.7 0 1 3 3 5 5 5 7 1.7 ≤ H< 1.8 1.75 8 1.8 0 0 0 1.8 ≤ H< 1.9 1.85 3

This distribution can be seen more easily by drawing a graph:

From the look of this graph, it can be assumed that the distribution of girls’ heights is skewed.  The skew is much more noticeable from this graph than from Box Plots.

Stem and leaf and Frequency Table (Boys Weight)

 Stem Leaf Range Midpoint Frequency 3 8 30 ≤ H< 40 35 1 4 0 2 2 4 5 5 5 5 7 8 40 ≤ H< 50 45 10 5 0 0 1 1 2 2 2 4 4 4 8 50 ≤ H< 60 55 11 6 0 0 0 0 0 3 4 5 6 6 60 ≤ H< 70 65 10 7 0 0 5 70 ≤ H< 80 75 3 8 5 80 ≤ H< 90 85 1

This distribution can be seen more easily by drawing a graph:

This graph looks slightly skewed, but there are too few data at the periphery of the distribution to be sure.

Stem and leaf and Frequency Table (Girls Weight)

 Stem Leaf Range Midpoint Frequency 3 6 7 8 8 30 ≤ H< 40 35 4 4 0 2 2 2 5 6 6 6 7 8 8 8 8 8 8 8 8 40 ≤ H< 50 45 17 5 0 0 1 1 1 2 2 2 2 2 4 4 4 5 5 7 7 8 8 50 ≤ H< 60 55 19 6 2 5 5 5 60 ≤ H< 70 65 4 7 - 70 ≤ H< 80 75 8 - 80 ≤ H< 90 85

This distribution can be seen more easily by drawing a graph:

From the look of this graph, it can be assumed that the distribution of boys’ weights is ‘normal’ since a single data point moving from the 55 to 45 would make the distribution symmetrical.

Standard deviation and confidence intervals

 Statistic Boys Height (m) Boys Weight (Kg) Girls Height (m) Girls Weight (Kg) Mean 1.59 50.02 1.63 55.08 Standard Deviation (SD) 0.10 10.65 0.086 7.19

Conclusion

This was also shown not to be true.

Hypothesis 2.c.

As the height increases, the weights will increase in proportion.

Although there seems to be a slight linear relationship, there is too much variability in the data and for boys, only 15% of the variability can be attributed to the variability in weight can be attributed to height and for girls, this becomes even less at almost 4%.

Evaluation

Overall, the results for the comparison of heights and weights were surprising.  I expected to see a much greater relationship between height and weight and a greater difference between boys and girls.

However, the distributions were as I expected.

If I were to do this project again, I would do the analysis taking account of the outliers.

Appendix 1 – The data

 Girls Boys Name Height (m) Weight (kg) Name Height (m) Weight (kg) Gemma 1.65 54 Herman 1.60 60 Ashley 1.65 48 Mahmood 1.56 60 Kathleen 1.7 52 Hosaib 1.66 54 Natalie 1.5 45 Hosiab 1.66 70 Hannah 1.62 52 Matthew 1.52 52 Amna 1.35 51 Khuram 1.75 75 Sonia 1.67 48 Pauya 1.65 45 Holly 1.63 47 Kurt 1.52 54 Rachael 1.56 50 Vintchenzo 1.67 54 Rachael 1.45 51 Albert 1.71 60 veronica 1.49 37 Steve 1.80 48 Victoria 1.75 65 Robin 1.73 66 Samantha 1.62 48 Stanley 1.55 50 Louise 1.51 48 Wayne 1.77 66 Tahira 1.62 42 Gary 1.73 52 Humspira 1.69 48 Jake 1.54 44 Nichola 1.36 38 Jon 1.47 42 Carol 1.58 55 Anthony 1.75 63 Ben 1.8 57 Andrew 1.62 40 Farrah 1.59 42 Andrew 1.46 45 Suzanne 1.6 46 John 1.80 64 Janine 1.62 54 Bob 1.50 70 Karen 1.6 46 Michael 1.61 38 Channan 1.59 52 Simon 1.54 60 Julie 1.59 50 Daniel 1.55 51 Stacey 1.55 57 James 1.54 42 Charelle 1.61 52 Jamie 1.80 51 Nichole 1.57 62 John 1.67 52 Rosie 1.5 65 Azhar 1.55 47 Suki 1.52 52 Jimmy 1.61 45 Louise 1.59 46 Tyler 1.70 85 Nicola 1.62 48 Tommas 1.58 65 Rose 1.61 38 John 1.60 58 Christine 1.64 42 William 1.65 50 Jade 1.57 48 Paul 1.53 45 Sarah 1.53 40 Simon 1.75 60 Caroline 1.59 48 Sandra 1.64 55 Louise 1.62 58 Amy 1.5 65 Kaylea 1.6 51 Samantha 1.71 54 Grebla 1.57 36 Belinda 1.53 58

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