# DATA HANDLING COURSEWORK

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Introduction

DATA HANDLING COURSEWORK

In this data handling coursework, I will be investigating the relationship between the heights and weights of pupils at Mayfield high school.

Mayfield high school is a fictitious high school with 1183 students. The information I have received from the Edexcel website, is however, based on a real school

If I am to consider the height and weight at Mayfield, I will need the following categories from the data provided:

- Height
- Weight
- Year Group
- Gender

I will split the coursework into 3 different lines of enquiries. These are: -

- Relationship between the heights and weights of students without considering any factors.
- Relationship between the heights and weights of students considering age.
- Relationship between the heights and weights of students considering gender.

I am investigating the relationship between the heights and weights of students because both variables are quantitative; therefore it is more logical to find a relationship between them.

I am investigating how age and gender affect the height and weight, and I am also investigating these factors to consider whether they affect the accuracy of my samples.

Due to the fact that taking any factors into account increases the accuracy of my analysis I will be able to focus on smaller sample sizes when investigating the data in strata.

I will use the method of stratified sampling because it takes into account all students of the different age ranges and genders from the school giving each pupil as equal chance as possible, so that the analysis can be as accurate and reliable as possible. There is no need to perform a random sample and a stratified sample as well because a random sample can

Middle

11

Male

1.64

60

Year Group | Gender | Height (m) | Weight (kg) |

7 | Female | 1.61 | 45 |

7 | Female | 1.62 | 40 |

7 | Female | 1.61 | 47 |

7 | Female | 1.65 | 45 |

7 | Female | 1.63 | 45 |

7 | Female | 1.58 | 50 |

7 | Female | 1.56 | 53 |

8 | Female | 1.44 | 49 |

8 | Female | 1.6 | 52 |

8 | Female | 1.6 | 45 |

8 | Female | 1.7 | 43 |

8 | Female | 1.59 | 44 |

8 | Female | 1.62 | 51 |

8 | Female | 1.65 | 41 |

9 | Female | 1.56 | 56 |

9 | Female | 1.8 | 62 |

9 | Female | 1.45 | 49 |

9 | Female | 1.58 | 55 |

9 | Female | 1.02 | 55 |

9 | Female | 1.68 | 36 |

9 | Female | 1.59 | 48 |

10 | Female | 1.6 | 9 |

10 | Female | 1.65 | 49 |

10 | Female | 1.65 | 42 |

10 | Female | 1.6 | 47 |

10 | Female | 1.55 | 48 |

11 | Female | 1.69 | 51 |

11 | Female | 1.63 | 48 |

11 | Female | 1.62 | 54 |

11 | Female | 1.72 | 51 |

I will now draw a scatter diagram including the line of best fit and the equation for both of my tables.

From the scatter diagram for the boys you can see that there is a positive correlation between the height and weight of these pupils. This tells me that the taller the person the more they will weigh.

Also, I can use my line of best fit to make predictions. The line of best fit suggests that a boy that weighs 70kg will be 1.7875m tall. I know this because I replaced the 70 in the formula as ‘x’ and then worked it out. I can also find the height of people that vary in weight.

I will now find the height of a boy that weighs 80kg.

If a boy weighed 80kg, he will be 1.8635m tall. So, from these two examples, I can say that the more the boy weighs the taller he will be.

I will now analyse the second graph which is for the girls. From the scatter diagram for the girls you can see that there is a positive correlation between the height and weight of these pupils. This tells me that the taller the person the more they will weigh.

Also, I can use my line of best fit to make predictions. The line of best fit suggests that a girl that weighs 70kg will be 1.6196m tall. I know this because I replaced the 70 in the formula as ‘x’ and then worked it out. I can also find the height of people that vary in weight.

I will now find the height of a girl that weighs 80kg.

If a girl weighed 80kg, he will be 1.6336m tall. So, from these two examples, I can say that the more the girl weighs the taller she will be.

However, if I now compare these two graph together I can come to the conclusion that the boys are taller than the girls, according to my sample. I am confident in saying this because as I have made prediction with the line of best fits, the height of the boys is taller than the girls for the same weight indicating that gender does affect the height and weight of a person.

So, from this I can conclude that the boys are taller and heavier than the girls. However, I will do the cumulative frequency and the box-plot diagram to further the investigation.

Firstly, I will find the measures of spread (mean, mode etc.) to analyse my results further.

Height | mean | median | modal class | range |

boys | 1.65 | 1.64 | 1.50<h<1.60 | 0.49 |

girls | 1.6 | 1.61 | 1.60<h<1.70 | 0.78 |

Weight | mean | median | modal class | range |

boys | 51.8 | 50.5 | 41-50 | 34 |

girls | 51.2 | 49 | 41-50 | 31 |

As you can see from this, I can clearly say that the boys are heavier and taller than the girls. I say this because the mean height for the boys is greater than the girls. Also, the range of the height is smaller for the boys meaning that most of them are tall. The mean height for the boys is also greater then the girls. This means that the boys are taller than the girls. Also, you can see that the mean weight for the boys is greater then the girls. This implies that most of the boys are heavier than the girls. In addition, you can also see that the median weight for the boys is greater than the girls’. This is also implying that the boys are heavier than the girls. So it seems to me, from the measures of spread, you can see that the boys are heavier and taller than the girls.

Now I will do the cumulative frequency. I will do this because; the cumulative frequency can be used to compare two sets of data. I will create cumulative frequency table for the weight of the boys and the girls, and then the cumulative frequency tales for height of the boys and girls. I will start of by doing the cumulative frequency table for the weight of the boys.

Weight (kg) (up to and including) | Tally | Frequency |

0 - 10 | 0 | |

11 - 20 | 0 | |

21 - 30 | 0 | |

31 - 40 | IIII | 4 |

41 - 50 | IIIIIIIIIII | 11 |

51 - 60 | IIIIIIIIIII | 11 |

61 - 70 | III | 3 |

71 - 80 | I | 1 |

81 - 90 | 0 | |

91 - 100 | 0 |

Now that I have done it for the boys, I will now do it for the girls.

Weight (kg) (up to and including) | Tally | Frequency |

0 - 10 | 0 | |

11 - 20 | 0 | |

21 - 30 | 0 | |

31 - 40 | I | 1 |

41 - 50 | IIIIIIIIIIIIIIII | 16 |

51 - 60 | IIIIIIIII | 9 |

61 - 70 | III | 3 |

71 - 80 | I | 1 |

81 - 90 | 0 | |

91 - 100 | 0 |

I will now join both of these tables to make it into one single table.

Cumulative frequency | ||

Weight (kg) (up to and including) | Boys | Girls |

0 - 10 | 0 | 0 |

11 - 20 | 0 | 0 |

21 - 30 | 0 | 0 |

31 - 40 | 4 | 1 |

41 - 50 | 15 | 17 |

51 - 60 | 26 | 26 |

61 - 70 | 29 | 29 |

71 - 80 | 30 | 30 |

81 - 90 | 30 | 30 |

91 - 100 | 30 | 30 |

I will now draw the cumulative frequency graph for the weight of the boys and the girls together.

This graph shows us many things. One of these things is that more girls than boys have weights that are up to 50kg. We can see this because the pink line is above the blue in the graph emphasising that more girls weigh less than boys.

Also, you can see that there are more girls that weigh between the range 41kg-50kg. This proves that more girls weigh less than boys. However, most of the girls and boys are between 41kg-50kg.

From the cumulative frequency graphs, I can also predict the percentage of boys or girls in the school between certain ranges. For example, I will now predict the percentage of boys and girls that weigh between 0kg and 50kg.

From the graph, I can see that 50% of the boys are between this range and 56.7% of the girls are between this range. So, from this I can now predict that 50% of the boys in the whole school will weigh between 0kg and 50kg, and that 57% of the girls in the whole school will be between this range. This implies that there will be a bigger percentage of boys than girls over this range proving that they are heavier than girls.

I will now do the cumulative frequency for the height of the boys and girls. Firstly, I will do the cumulative frequency tables for the boys.

Height, h (cm) | Tally | Frequency |

1.30<h<1.40 | I | 1 |

1.40<h<1.50 | II | 2 |

1.50<h<1.60 | IIIIIIIIII | 10 |

1.60<h<1.70 | IIIIII | 6 |

1.70<h<1.80 | IIIIIII | 7 |

1.80<h<1.90 | IIII | 4 |

Now that I have done it for the boys, I will now do it for the girls.

Height, h (cm) | Tally | Frequency |

1.00<h<1.10 | I | 1 |

1.10<h<1.20 | 0 | |

1.20<h<1.30 | 0 | |

1.30<h<1.40 | 0 | |

1.40<h<1.50 | II | 2 |

1.50<h<1.60 | IIIIIIIIIII | 11 |

1.60<h<1.70 | IIIIIIIIIIIII | 14 |

1.70<h<1.80 | II | 2 |

1.80<h<1.90 | 0 |

Conclusion

From the graphs I can also say that the older they get, the heavier they get. This is also proven in both graphs. As you can from both graphs, the yellow points are furthest to the right, and the blue points are towards the left, leaving the pink points in the middle. This shows that as the child is getting older he is gaining more weight.

In conclusion, I have proven, from my sample, that as the child gets older, he will gain more weight. In addition, the child will also get taller.

Conclusion

I have now completed my investigation at Mayfield high school. I followed the following lines of enquiries: -

- Relationship between the heights and weights of students without considering any factors.
- Relationship between the heights and weights of students considering age.
- Relationship between the heights and weights of students considering gender.

I can now make conclusions and comment on my predictions and the investigation.

I can say without any doubt, that the taller the person got, the more the weighed. This was proven to you by my first line of enquiry. My prediction was also correct.

Moreover, I have proven to you from the sample I had, that the boys at Mayfield high school were taller and heavier than the girls. This was shown to you in my second line of enquiry. My prediction was also correct.

Furthermore, I have also found out that as the person gets older, the person will get taller and heavier. This is shown to you in the third line of enquiry. My prediction was also correct.

Therefore, I can conclude by saying my investigation was a success.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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