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  • Level: GCSE
  • Subject: Maths
  • Word count: 3240

Investigate an even proportion of the pupils at Mayfield High school and draw up various graphs to help support my hypothesis, investigating the relationship between the height and weight of these pupils.

Extracts from this document...

Introduction

Maths Coursework: Data Handling Project

(Of “Mayfield High School”).

Introduction:

I am going to investigate an even proportion of the pupils at Mayfield High school and draw up various graphs to help support my hypothesis, investigating the relationship between the height and weight of these pupils. I expect that the relation between the height and weight of the sampled pupils to be that generally their weight will increase with their height. To be able to achieve this I will need to collect data to support or contradict this. The data I will collect will come from a booklet of data so therefore it will be secondary data because I have not gone to collect the data myself. I think I will require the data of 10% of the pupils at Mayfield because I feel that 10% will be comparatively easy to handle and will give enough data from the total 1200 pupils (10% will be 120 of them) to form a good set of data resembling as much as possible all the pupils of Mayfield. I could have chosen a smaller sample size to make the investigation easier but this would result in the project being less accurate and then again I could also have chosen a larger sample size to make the project more accurate but this would obviously result in more data being sampled and therefore making it more difficult to investigate: there would be too much data to analyse and draw sensible conclusions from. To do this I will take a stratified sample of all the pupils (so that I can compare like with like) showing how I did it; without

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Middle

10

10

20

11

8

9

27

Total sample size is 120 (10% of 1200).

Method:

My hypothesis is that as the pupils increase in height they increase in weight. I have put together graphical evidence to help prove this.

        To start with I shall look at year 7: to give a straight forward impression of this year I have created scatter graphs showing height against weight.

Year 7 Boys:

This plainly shows that there is a strong positive correlation of height against weight. This correlation would however be stronger had it not been for a certain ‘outlier’ (a piece of data which does not relate in proportion to the rest of the data it is with in the top left hand corner in this case). The graph following this one demonstrates my point: it is the same graph but without the outlier.image00.png

The difference is not huge but it shows that it does not take much to influence a set of data. I will not refer to this graph, though, as it is now biased – as I am fiddling the data to help fit my hypothesis better.image01.png


Year 7 Girls:        

This graph is very similar to the boys of this year, with the average (the pink spot) being slightly less than the boys. The equations of the linear trend lines represent this similarity:image02.png

Boys: y = 0.0028x + 1.4347

If x is 30, y = 1.5187

Girls: y = 0.007x + 1.22

 If x is 30, y = 1.43.

        This strong positive correlation shown in those last two graphs is very similar throughout all the different year groups and sexes apart from two of them and I have an explanation for this. These are the two graphs:

        As you can see, both graphs seem to have a slight negative correlation and particularly the year 10 boys have their data points scattered all over the place – all the points are apparently outliers. image03.png

        Well,

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Conclusion

I finally conclude that the taller the pupils at Mayfield High School the heavier they become (but to find out whether my data produces evidence solid enough to support this conclusion, I would have to perform a statistical test).

To illustrate my conclusion generally I have produced a scatter graph with my entire data sample on it and it clearly shows that there is a strong positive correlation between the height and the weight of the pupils at Mayfield:

image06.png

Evaluation:

This investigation could be improved in several different ways.

        To start with: I could have made my data more accurate and reliable by choosing a bigger sample size and collecting my data sample by using random stratified sampling instead of systematic stratified sampling. This would increase the credibility of my data and hence my conclusion.

        I could have made more use of different averages to support my hypothesises such as the median, interquartile range and the range (but not the mode as the data I analysed was continuous and single values are unlikely to occur more than once). More use of standard deviation appropriately would have helped as well.                

        To get unbiased data I used stratified sampling as this collects the correct ratio of boys to girls in a data sample compared to the original set of data. I have used a range of different diagrams to characterize my data and have also included standard deviation to increase the credibility of my data. I have also added a couple of diagrams in my conclusion to illustrate the conclusion.

        Practical uses for my data could be: because my data suggests that height increases with weight generally it could be used by clothes designers to design the appropriate sized clothes.

        My data could also be used for estimating the height or weight of a particular person when given only the height or weight of that person.  

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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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