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GCSE Mathematics Coursework: Statistics Project

Extracts from this document...

Introduction

Chioma Oganya, 11F Tiffin Girls’ School

GCSE Mathematics Coursework: Statistics Project

Introduction

Mayfield is a fictitious High School that features data on the 1150 pupils in Years 7 – 11.  The data presented is based on a real school and includes information such as gender, year group, IQ, height and weight for each pupil.  My aim is to analyse this information to prove the following hypothesis:

The more hours of TV watched per week, the greater the weight of the pupil.

Justification of Hypothesis:

It is logical to assume that the more time spent sitting in front of the television, the less time spent on active activities such as exercise and sport.  Therefore, I think that people that watch large amounts of television will be more unfit and will consequently weigh more as they have not participated in much vigorous exercise to ‘burn off’ fat.

Table showing the Number of Boys and Girls in each Year Group of Mayfield High School

Year Group

Number of Boys

Number of Girls

Total

Year 7

151

124

275

Year 8

141

119

260

Year 9

112

141

253

Year 10

103

92

195

Year 11

82

85

167

Total

589

561

1150

With a database featuring 1150 pupils, it would be impractical to analyse the entire database considering the time constraints.  I will need to take an appropriate sample so that I can analyse the information to come to a reliable conclusion.  A sample of 100 pupils is appropriate as it is large enough for any findings to be reliable (in contrast, if a conclusion was formed using data from only six pupils for example, then it would not be reliable as the sample would not be fully representative of all the pupils in the school).  It is important to make sure that the sample is not biased, so that the conclusion is reliable.  The school features Years 7 – 11 and in each year, there are different numbers of girls and boys.

...read more.

Middle

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to get random numbers ranging from 0 < x ≤ 276.  276 must be used rather than 275, as Row 1 is used in every Excel sheet for the list headings, rather than holding a pupil’s data.  Therefore, if the number ‘1’ was randomly generated, it would be ignored and the random number ‘276’ would mean I would take the pupil in Row 276, which would be pupil no. 275.  Obviously, I will continue to take pupils in Year 7 until I have 13 boys and 11 girls.  If, for instance, a number is generated where the pupil is female even after 11 girls have already been selected, then the number will be ignored.  Otherwise, the proportions of girls and boys in the sample would not represent the proportions present in the Year Group.  Also, as the random numbers generated can be up to three decimal places, they will be rounded to the nearest whole number.

After performing this process for Year 7, the same will be done for each Year group to select the pupils.

I have now collected my sample, which is shown overleaf:

In order to test whether there is a relationship between the average amount of TV watched per week and the weight of a pupil, I will construct a scatter graph.  Scatter graphs are effective in discovering whether there is a correlation between two sets of data, as one set of data is plotted on the x-axis and the other on the y-axis.  A line of best fit can also be drawn and the r-value can be found using Excel to describe how strong the correlation is.  For my scatter graph, the average hours of TV watched per week will be on the x-axis, as my hypothesis states that this will determine the weight of a pupil.  

...read more.

Conclusion

Conclusion – Has my hypothesis been proved or disproved?

It has been proved to a certain extent.  The Year 7s and Year 8s in the sample show that the more TV a pupil watches, the more he/she weighs.  However, Years 9-11 show otherwise and when looking at the relationship between the amount of TV watched and weight for the sample of 100, it appears that the more TV pupils watch, the less they weigh.  Gender has also proved to affect the relationship, with girls generally watching slightly more than boys but weighing less.


what do I want 2 do         – analyse weight using mean + standard deviation

  • analyse the amount of TV by doing a box and whisker diagram.. to find the median + the interquartile ranges, first will group the data into categories + will do cumulative frequency diagrams, one for the females + one for the males.
  • Then do the years…

The graph shows….Grouping the 100 pupils together might hide differences between different groups, such as females and males.  To discover whether there is a difference in correlation between the boys’ weight compared to the amount of TV watched and the girls’ weight and the amount of TV watched, separate scatter graphs will be plotted for the 51 boys and the 49 girls…

  • note the differences in r-values
  • also note that the girls generally watch far less tv – this will be interesting to analyse in a box + whisker + cumulative frequency diagram.

Fall back on this:

This graph features data from all the people in the sample of 100, so the results may hide slight differences between certain groups ie girls may generally watch more television than boys, or there might be a stronger correlation between amount of TV watched and weight for Year 7s than Year 11s.  In order to investigate this, I will first test whether there is a difference in the relationship between the amount of television and weight for boys and then girls, by doing one scatter graph for the 51 boys and another for the 49 girls.

...read more.

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