# "The taller the pupil, the heavier they will weigh."

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Introduction

Introduction

MayfieldSchoolis a secondary school of 1183 pupils aged 11-16 years of age. For my data handling coursework I have got to investigate a line of enquiry from the pupils' data. Some of the options include; relationship between IQ and Key Stage 3 results, comparing hair colour and eye colour, but I have chosen to investigate the relationship between height and weight. One of the main reasons being that this line of enquiry means that my data will be numerical, allowing me to produce a more detailed analysis rather than eye or hair colour where I would be quite limited as to what I can do.

If I were to make an original prediction of my results, my hypothesis would be;

"The taller the pupil, the heavier they will weigh."

In this project I will consider the link between height and weight and will eventually be able to state whether my original hypothesis is in fact correct. Other factors I am going to consider when performing this investigation, is the effect of age and gender in my results and I will make further hypothesize when I reach that stage in my project.

Collecting Data

I have originally decided to take a random sample of 30 girls and 30 boys; this will leave me with a total of 60 pupils. I have chosen to use this amount as I feel this will be an adequate amount to retrieve results and conclusions from, although on the other hand it is not too many which would make my graph work far more difficult and in some cases harder to work with. To retrieve my data I am

Middle

Frequency

Weight, w (kg)

Frequency

20 ≤ w < 30

2

20 ≤ w < 30

0

30 ≤ w < 40

4

30 ≤ w < 40

3

40 ≤ w < 50

13

40 ≤ w < 50

11

50 ≤ w < 60

8

50 ≤ w < 60

7

60 ≤ w < 70

3

60 ≤ w < 70

4

70 ≤ w < 80

0

70 ≤ w < 80

2

80 ≤ w < 90

0

80 ≤ w < 90

3

Height Frequency Tables

GirlsBoys

Height, h(cm) | Frequency | Height, h(cm) | Frequency |

120 ≤ h < 130 | 1 | 120 ≤ h < 130 | 0 |

130 ≤ h < 140 | 1 | 130 ≤ h < 140 | 1 |

140 ≤ h < 150 | 3 | 140 ≤ h < 150 | 1 |

150 ≤ h < 160 | 8 | 150 ≤ h < 160 | 11 |

160 ≤ h < 170 | 13 | 160 ≤ h < 170 | 7 |

170 ≤ h < 180 | 4 | 170 ≤ h < 180 | 2 |

180 ≤ h < 190 | 0 | 180 ≤ h < 190 | 6 |

190 ≤ h < 200 | 0 | 190 ≤ h < 200 | 2 |

Because both height and weight are continuous data, I have chosen to group the data in class intervals of tens as this allows me to handle large sets of data more easily and will be easier to use when plotting graphs. In both the height and weight column, '120 ≤ h < 130', this means '120 up to but not including 130', any value greater than or equal to 120 but less than 130 would go in this interval. I feel I am now at the stage where I can go on to record my results in graph form. This will then allow me to analyse my data and compare the results for the differing genders, which I am unable to do with the tables above.

Weight

As I mentioned earlier both height and weight are continuous data so I cannot use bar graphs to represent it, instead I will have to use histograms as this is a suitable form of graph to record grouped continuous data. Before I produce the graph I am going to make another hypothesize that;

"Boys will generally weigh more than girls."

Histogram of boys' weights

Histogram of girls' weights

Obviously by looking at the two graphs I can tell there is a contrast between the girls' and boys' weights, but to make a proper comparison I will need to plot both sets of data on the same graph. Plotting two histograms on the same page would not give a very clear graph, which is why I feel by using a frequency polygon it will make the comparison a lot clearer.

Frequency polygons for boys' and girls' weights

This graph does support my hypothesis, as it shows there were boys that weighed between 80kg and 90 kg, where as there were no girls that weighed past the 60kg-70kg group. Similarly there were girls that weighed between 20kg and 30kg were as the boys weights started in the 30kg-40kg interval. Although by looking at my graph I am able to work out the modal group, but it is not as easy to work out the mean, range and median also. To do this I have decided to produce some stem and leaf diagrams as this will make it very clear what each aspect is, for the main reason I will be able to read each individual weight - rather than look at grouped weights. Stem and leaf diagrams show a very clear way of the individual weights of the pupils rather than just a frequency for the group-which can be quite inaccurate.

GirlsBoys

Stem | Leaf | Frequency | Stem | Leaf | Frequency | |

20 kg | 9,9 | 2 | 20 kg | 0 | ||

30 kg | 6,6,8,8 | 4 | 30 kg | 2,8,9 | 3 | |

40 kg | 0,2,2,5,5,5,5,5,7,7,8,8,9 | 13 | 40 kg | 0,3,4,5,5,5,6,7,7,7,8 | 11 | |

50 kg | 0,0,0,1,1,1,2,2 | 8 | 50 kg | 0,0,1,1,2,4,4 | 7 | |

60 kg | 0,0,0 | 3 | 60 kg | 0,0,0,4 | 4 | |

70 kg | 0 | 70 kg | 0,0 | 2 | ||

80 kg | 0 | 80 kg | 0,0,2 | 3 |

From this table I am now able to work out the mean, median, modal group (rather than mode because I have grouped data) and range of results. This is a table showing the results for boys and girls;

Weights (kg) | Mean | Modal Class | Median | Range |

Boys | 50 kg | 40-50 kg | 50 kg | 50 kg |

Girls | 46 kg | 40-50 kg | 47 kg | 31 kg |

Conclusion

I have now reached a point in my investigation where my random sample of 30 boys and girls is not necessary anymore. There have definitely been some clear conclusions made from my graphs and tables already, which have all in fact fitted in with my predictions made. However my predictions are only based on general trends observed in my data, and in both the girls and boys samples there were individuals whose results did not fit in with the general trend. I cannot have complete confidence in my results so far due to the fact this is only a random sample of 30 girls and boys and age has not been considered which I now feel is a necessary factor. I have spent a good amount of time considering different genders but now I am going to look at age differences. It is only common sense that age is going to affect your height and weight, for you would think a year 7 pupil would be smaller and lighter than a pupil in year 11. As Mayfield is a growing school there would be more pupils in year 7 than in year 11, therefore my random sample was likely to contain more year 7 pupils than year 11 - this is biased and unfair. To ensure that I obtain a data set with an accurate representation of the whole school, I am going to have to take a stratified sample. Stratified sample means that you sample a certain amount from a particular group to proportion that group's size within the whole population, i.e. pupils within year 8, within the whole school.

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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