Mayfield High School Project

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Mithun Rama  GCSE Mathematics Statistics Courseowork

Mayfield High School Project

Introduction

Mayfield High School is a secondary school of 1183 pupils aged 11-16 years of age. There are 603 male pupils and 580 female pupils at this school. For my Data Handling Coursework, I will be investigating a line of enquiry from the pupils' data. Some of the options include the relationship between IQ and Key Stage 2 results, comparing hair colour and eye colour. However, 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 prove 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 going to firstly use a random sample as this means that my data is not biased in any way, and all of the pupils will vary in height, weight and age - although I will have an equal gender ratio. Random sampling is a sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has a known, but possibly non-equal, chance of being included in the sample.

An easy way of performing this task is by using the 'Random' button on my calculator. To retrieve 30 random numbers I would have to input; 2ndF, Random, (580) for the female pupils and change the 580 to 603 for the male pupils. This then means that the calculator will give me 30 whole numbers within the range of 1-580 or 1-603. The random sample that I obtained is shown in the table on the following page.

I need a more useful representive of the data shown above, so I have decided to sort my data out and put it into height and weight frequency tables. This will allow me to see the data far more clearly and it will allow me to plot graphs from the data with less difficulty.

Height Frequency Tables

Weight Frequency Tables

As 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 a graphical format. 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 a further hypothesis 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 that there is a contrast between the male and female 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.

This graph does support my hypothesis that the male pupils will generally weigh more than the female pupils, as it shows there were male pupils that weighed between 80kg and 90 kg, where as there were no female pupils that weighed beyond the 60kg-70kg group. Similarly there were female pupils that weighed between 20kg and 30kg were as the male pupils weights started in the 30kg-40kg interval. I am not going to include the male pupil, that is in the 0kg-10kg interval, in this analysis because I believe that this is not possible for a pupil in secondary school to be of this weight which is why I am calling this value an outlyer. 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.

Stem and Leaf Diagram for Male Pupils Weight:

0: 9

10:

20:

30: 2, 8,9

40: 0, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8

50: 0, 0, 1, 4

60: 0, 0, 0, 0, 4

70: 0, 0, 4

80: 0, 0, 2

90:

Stem and Leaf Diagram for Female Pupils Weight:

0:

10:

20: 9, 9

30: 6, 6, 8, 8

40: 0, 2, 2, 5, 5, 5, 5, 5, 7, 7, 8, 8, 9

50: 0, 0, 0, 1, 1, 1, 2, 2

60: 0, 0, 0

70:

80:

90:

From the diagrams above, 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 both male and female pupils;

Join now!

Despite both male and female pupils having the majority of their weights in the 40-50kg interval, 11 out of 30 male pupils (37%) fitted into this category whereas 13 out of 30 female pupils (43%) did which is easily seen upon my frequency polygon. I could not really include that in supporting my hypothesis as the other aspects do. My evidence shows that the average male pupil is 7.3kg heavier than that of the average female pupil, and also that the median weight for the male pupils is 3.1kg above that of the female pupils. Another factor my sample would ...

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