# Data Handling Project

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Introduction

Maths Coursework – Mayfield High School - Mrs Ferguson

Data Handling ProjectAlexandra Mullan

For this project, I have chosen to show the relationship between height and weight. The main reason for this is because the data for height and weight is continuous, unlike eye and hair colour and KS2 results which are discrete or qualitative. Therefore, I can put the information I find into cumulative frequency tables, box plots, histograms and scatter graphs.

Plan

Before I begin my statistical inquiry I need a hypothesis to examine. A hypothesis is used as a basis for further investigation, and my first hypothesis is going to be as follows:

“The taller a pupil is, the more they are going to weigh “

I will use scatter graphs to compare all of my data and find correlations and standard deviation. I will use my histograms and box and whisker plots to investigate further the weight differences between each year and the boys and girls, and therefore I will find the quartiles and the median etc.

I could do this investigation using all 1183 pieces of data; however this would be extremely time-consuming. I therefore am going to take a random stratified sample, and if I make my sample large enough I am confident that the results will give a good indication of the results as a whole because my data will have a large range and should consequently cover a good majority of heights and weights.

By sampling, I simplify my calculations and graphs dramatically. However, I must make sure that the sample I take is completely unbiased otherwise my results will be corrupt.

Before I begin my study, I will create a scatter graph comparing random people’s height and weight so that I can see whether the hypothesis is worth investigating.

Middle

Jones

Brian

1.32

38

9

Rowley

Geoff

1.56

53

10

Bates

Markus

1.80

60

10

Edd

Michael

1.68

59

10

Javidson

Carlos

1.70

57

11

Fairfax

Jacob

1.62

51

11

Little

James

1.65

47

11

Vincent

Nigel

1.8

62

At first, I thought about only putting the heights and weights down, and leaving out the names. However, I realised then that I would have no proof that the data I have come up with is real. Without the names, I would find it difficult to prove that I had not tampered with the data in order to make my hypothesis true. It was acceptable when doing my initial scatter graph because it was initial research to see whether my hypothesis was worth investigating or not.

Stratified Sample Results – Girls

Year Group | Surname | Forename 1 | Height (m) | Weight (kg) |

7 | Butler | Leanne | 1.65 | 40 |

7 | Earnshaw | Catherine | 1.45 | 41 |

7 | Meager | Becky | 1.64 | 47 |

7 | Miles | Amanda | 1.46 | 40 |

7 | Richards | Abbie | 1.53 | 47 |

8 | Burton | Prudence | 1.59 | 52 |

8 | Campbell | Julia | 1.41 | 30 |

8 | Kudray | Rebecca | 1.54 | 52 |

8 | Water | Rebecca | 1.55 | 57 |

9 | Atkins | Patience | 1.57 | 40 |

9 | Bagnall | veronica | 1.49 | 37 |

9 | Dixon | Mary | 1.49 | 52 |

9 | Kelsey | Sannita | 1.62 | 46 |

9 | Mosler | Samantha | 1.58 | 36 |

10 | Bhatti | Hannah | 1.72 | 56 |

10 | Durst | Freda | 1.75 | 60 |

10 | Hall | Jane | 1.51 | 36 |

11 | Marta | Sana | 1.52 | 45 |

11 | Ratty | Louise | 1.65 | 59 |

11 | Peckeleka | Chantel | 1.56 | 38 |

Now that I have my data I will put them into frequency tables because it is a useful way of representing the data and it makes it easier to view trends within the data that I have collected.

Also, I am going to change the height unit from metres (m) to centimetres (cm). I am doing this because it will make it easier to create the frequency tables, and also it will increase the chances of me spotting a trend within the data.

Boys – Height

Height (cm) | Frequency |

130≤h<140 | 2 |

140≤h<150 | 0 |

150≤h<160 | 6 |

160≤h<170 | 8 |

170≤h<180 | 1 |

180≤h<190 | 3 |

190≤h<200 | 0 |

A pattern I have spotted in this particular frequency table is that nearly 75% of boys are between 150cm and 170cm. This shows me that students in my sample are rather tall, and as it is the majority that are taller, it means that boys of their age are generally tall.

Girls – Height

Height (cm) | Frequency |

140≤h<150 | 5 |

150≤h<160 | 9 |

160≤h<170 | 4 |

170≤h<180 | 2 |

180≤h<190 | 0 |

This table shows me that nearly 50% of female students are between the height of 150cm and 160cm, and there are not many female students who excel over 180cm. Also, there were not many girls with a height between 130cm and 140 cm, which shows me that the spread of data is compact, making it easier to view trends and also it shows that there are not many irregularities in height in the student sample that I have taken.

Comparison

From the sample I have taken, I have found that boys grow rapidly at a later age whereas girls grow faster from an earlier age, and then stop at a particular age. Both girls and boys have average heights, and are fairly balanced / are of equal size. My sample shows that boys on some occasions grow to above average height, such as over 180 cm, whereas in girls this is rare and unique.

Boys – Weight

Weight (kg) | Frequency |

30≤w<40 | 4 |

40≤w<50 | 7 |

50≤w<60 | 6 |

60≤w<70 | 3 |

70≤w<80 | 0 |

This frequency table shows the boys weights and the spread of data are large, and not as compact as the height; the heights are rather scattered and varied. This, however, notifies me that some of the students in my sample are tall for their age, but their weights are average in relationship to their height.

Girls – Weight

Weight (kg) | Frequency |

30≤w<40 | 5 |

40≤w<50 | 8 |

50≤w<60 | 6 |

60≤w<70 | 1 |

70≤w<80 | 0 |

From this frequency table, I have found that many girls weigh between 40kg and 49kg, and also that hardly any girls weight more than 60kg. This shows me that some girls may stop putting on weight rapidly after a particular age.

Comparison

Most boys and girls from my sample weigh between 40kg and 60kg. I have found that not many girls are over the weight of 60kg, whereas boys are usually borderline 60 or above when they come to the age of 16.

Mean of Frequency Data

I will now calculate the mean of the frequency data that I have found, and this will be quick, efficient and reliable. It will help me to gain evidence on my hypothesis: whether boys are taller and weigh more in comparison to girls.

Frequency Table – Boys Weight

Weight (kg) | Frequency (f) | Mid-point (x) | fx |

30≤w<40 | 4 | 35 | 140 |

40≤w<50 | 7 | 45 | 315 |

50≤w<60 | 6 | 55 | 330 |

60≤w<70 | 3 | 65 | 195 |

70≤w<80 | 0 | 75 | 0 |

TOTAL | 20 | 980 |

Conclusion

Evaluation of Hypothesis

In my honest opinion, I feel that I successfully completed and analyzed my hypothesis and have gained a sufficient evidence to back up my theories. I would like to remind you that my main objective for this hypothesis was to find out whether I was correct or incorrect in my thinking that boys at Mayfield School are taller and weigh more on average than the girls at the same school. Within this aim, I was also aiming to find whether there is a certain trend or relationship between the height and weight of the students that I have chosen to analyse. Also, as I explained earlier, due to the large number of students I was unable analyse all students. Therefore, I gained a sufficient sample which I made as unbiased as possible, and got my results from the pieces of data that I randomly collected.

Conclusion of Hypothesis

- The histograms and frequency polygons proved that the results were more accurate, and made more sense than that from the random sampling.

- There is a positive correlation between height and weight. In general, tall people will weigh more than smaller people.

- In general, boys tend to weigh more and be taller than girls.

- By doing stratified sampling, there were fewer exceptional values caused by different year groups and, therefore, ages. I was bound to find irregularities within my data from the start.

- The cumulative frequency curves confirm that boys have a more spread out range in weight, with more girls having smaller weights. In height, boys tend to be taller.

- In general the taller a person is, the more they will weigh.

- There is a positive correlation between height and weight across the school as a whole. This correlation seems to be stronger when separate genders are considered.

- If I had taken larger samples my hypothesis may become more accurate.

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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.

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