Maths Statistics Coursework: Mayfield High

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Math’s Coursework: Mayfield High

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. I have chosen to investigate the relationship between height and weight. One of the main reasons for choosing this line of enquiry is that my data will be Quantitative and Continuous, allowing me to produce a more detailed analysis rather than eye or hair colour- which are qualitative/categorical data where I would be quite limited as to what I can do.

Line of Enquiry: The relationship between Height and weight of pupils

If I was to make a hypothesis for the result, it would be: The taller the pupil, the heavier they will weigh.

For My coursework, I have chosen a sample size of 50 students; 25 of which will be girls and the other 25 will be boys. 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 may be a little number compared to the population size and hence could be unreliable.

To retrieve my data I am going to firstly use stratified sampling - A stratified sample takes a proportional number from each group in the population so that each group is fairly represented.  This is necessary when producing graphs or statistical calculations on more than one section of the population together.  Then once I’d got my stratified sample for each group, I am going to 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. 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.

Stratified sampling

To carry out my Stratified sampling, I used the following method.

In this case, the size of the population is 1183 whilst the size of the sample is 50

Year 7 Boys _                

151

-----     X 50 = 6

1183

Year 8 boys

145

1183   x 50 =6          

         

Year 9 Boys

118

1183   x 50 = 5          

Year 10 Boys

106

1183   x 50 = 4

Year 11 Boys

  84

1183   x 50 = 4

Once I’d known how many pupils I will need to sample from each year, I then performed a random 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 enter the population (1183) and then press the ‘SHIFT’ button. Then I would have to press the ‘Ran#’ button.  As a result I would have the following formula on my calculator: 1183RAN#

As I need a more useful representative of the data shown above, 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. 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.

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Height Frequency Tables

Weight Frequency Tables

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;

"In general the boys will be of a greater height than the girls."

Frequency Diagram of boys' heights

Frequency Diagram of girls' heights

As ...

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