# Mathematics Statistics Coursework

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Introduction

GCSE Mathematics Jaitej Walia 10K

Statistics Coursework 8 November 2008

GCSE Mathematics Statistics Coursework

A. Introduction

My Task is about intelligence. The questions that I am going to investigate are:

1. -The mean of boys and girls in SATS scores.

-The area/frequency of boy’s and girls SATS score.

2. -The correlation and relationships between the IQ of Year 7 Boys and Girls, Year 11 Boys and Girls; and also the SATS scores of Year 7 and 11 Boys and Girls.

-What happens to the frequencies as the IQ and SATS scores goes higher?

B. Hypotheses

The hypotheses I will be testing are whether

-Boys do better in SATS than girls

- The higher the IQ, the higher the average SATS score.

I think that these hypotheses are true as boys, historically, have a better mean than girls, and if you are more intelligent than someone, (calculating from your IQ), you will do better in your SATS.

C. Plan of Action – Data Collection

I will need to collect the data from Mayfield High School. The data I will need to collect are “Year 7’s boys; Year 7 girls; Year 11 boys; Year 11 girls” data. This data will be useful as I can use and explain a wide range of data from both genders and I can conclude the intelligence of elder and younger pupils. I will only collect a little data from each data group e.g. 20 pupil’s data from the “Year 11 girls” data group. I will need to take a sample from the population, as it’ll be quick as well, instead of using the whole population’s data. I will take a stratified sample as this is a fair method, and it isn’t biased as it is random. I will be using secondary data, as I am going to take data from another source.

Middle

5

106

4

5

5

5

50

7

Carol-Mcardle

Lauren

Jill

12

4

106

5

4

5

5

214

7

Pledge

Jessica

11

11

128

5

5

5

5

43

7

Butler

Leanne

12

2

107

4

4

5

4

236

7

Smith

Mary

Ann

12

4

100

4

4

4

4

263

7

Vickers

Holly

12

9

103

4

4

4

4

123

7

Hughes

Karen

12

1

132

5

5

5

5

67

7

Craft

Clara

12

9

96

3

3

4

3

This table has the relevant and important pieces of data of 22 random Year 7 girls, which will be used in diagrams, charts, graphs and calculations to find the answers to my questions and to provide information for my original hypotheses.

Year 11 Boys

Pupil No | Year Group | Surname | Forename 1 | Forename 2 | Years | Months | IQ | English | Maths | Science | Average SATS Score |

331 | 11 | Oliver | Marcus | 16 | 5 | 99 | 4 | 4 | 3 | 4 | |

317 | 11 | McGuire | Frederick | 16 | 7 | 89 | 3 | 4 | 3 | 3 | |

282 | 11 | Hussain | Muhammad | 16 | 4 | 90 | 4 | 3 | 3 | 3 | |

347 | 11 | Simmons | Russell | Scott | 16 | 9 | 108 | 5 | 5 | 5 | 5 |

315 | 11 | McDonald | James | Harold | 16 | 2 | 122 | 5 | 5 | 5 | 5 |

286 | 11 | Johnes | Jimmy | James | 16 | 2 | 114 | 5 | 6 | 5 | 5 |

331 | 11 | Oliver | Marcus | 16 | 5 | 99 | 4 | 4 | 3 | 4 | |

358 | 11 | Spern | Jon | 16 | 4 | 96 | 4 | 3 | 3 | 3 | |

307 | 11 | Mamood | Keith | Norman | 16 | 3 | 94 | 3 | 4 | 4 | 4 |

306 | 11 | Major | William | Brian | 16 | 0 | 99 | 4 | 4 | 4 | 4 |

264 | 11 | Frost | James | Jackson | 16 | 2 | 107 | 5 | 4 | 6 | 5 |

223 | 11 | Boggart | john | 16 | 5 | 76 | 2 | 2 | 3 | 2 | |

307 | 11 | Mamood | Keith | Norman | 16 | 3 | 94 | 3 | 4 | 4 | 4 |

214 | 11 | Berk | Stephan | Donald | 16 | 5 | 119 | 5 | 5 | 5 | 5 |

This table has the relevant and important pieces of data of 14 random Year 11 boys, which will be used in diagrams, charts, graphs and calculations to find the answers to my questions and to provide information for my original hypotheses.

Year 11 Girls

Pupil No | Year Group | Surname | Forename 1 | Forename 2 | Years | Months | IQ | English | Maths | Science | Average SATS Score |

270 | 11 | Hakins | Danielle | Louise | 16 | 1 | 100 | 4 | 4 | 4 | 4 |

257 | 11 | Feehily | Christina | Jean | 16 | 6 | 112 | 4 | 4 | 4 | 4 |

217 | 11 | Bertwistle | Lara | Alyson | 16 | 8 | 126 | 6 | 6 | 6 | 6 |

288 | 11 | Jonson | Kirten | Nichole | 16 | 8 | 100 | 4 | 4 | 4 | 4 |

254 | 11 | Durst | Francesca | Celine | 16 | 4 | 95 | 4 | 3 | 4 | 4 |

224 | 11 | Bradbury | Natalie | Angela | 16 | 9 | 91 | 4 | 3 | 3 | 3 |

270 | 11 | Hakins | Danielle | Louise | 16 | 1 | 100 | 4 | 4 | 4 | 4 |

308 | 11 | Margeus | Nichola | Paula | 16 | 10 | 100 | 4 | 4 | 4 | 4 |

245 | 11 | Dawson | Jane | Samantha | 15 | 11 | 101 | 5 | 5 | 5 | 5 |

245 | 11 | Dawson | Jane | Samantha | 15 | 11 | 101 | 5 | 5 | 5 | 5 |

204 | 11 | Ali | Amera | 15 | 0 | 90 | 4 | 4 | 4 | 4 | |

336 | 11 | Peterson | Louise | Gemma | 16 | 7 | 91 | 3 | 3 | 3 | 3 |

246 | 11 | Dion | Dawn | Stella | 16 | 1 | 104 | 4 | 4 | 5 | 4 |

324 | 11 | Mustaq | Sumreen | 16 | 11 | 107 | 4 | 4 | 5 | 4 | |

369 | 11 | Wilson | Charlene | Astley | 16 | 9 | 87 | 4 | 2 | 3 | 3 |

This table has the relevant and important pieces of data of 15 random Year 11 girls, which will be used in diagrams, charts, graphs and calculations to find the answers to my questions and to provide information for my original hypotheses.

E. DataCollection

I have collected all my data I planned to collect from Mayfield High School students. I didn’t experience any problems collecting my data as it was collected using a macro from a spreadsheet. I have included my data in a summary table as I have only included the relevant data for my hypotheses and questions that I will investigate.

My tables do have clear headings as they are typed out in bold. All my headings are relevant to what I need. I added another heading, ‘Average SATS Score’, as when a graph, chart or a diagram is shown, there are only two axes, not four. So I have to make an average of every three different SATS Scores for one student.

Conclusion

The Cumulative Frequency Diagrams showed us that as the IQs and Average SATS Scores go up, the Frequencies go up, but stop at the end. This was the same in both IQ Cumulative Frequency Diagram and Average SATS Score Cumulative Frequency Diagram. So as the IQ increases, it showed us that the higher the IQ, the better you’ll do in your SATS; or the higher your Average SATS Score, the better your IQ will be.

This means that my second hypothesis was correct, as the scatter graphs and cumulative frequency diagrams provided information to explain the reason for it to be correct.

Evaluation

My strategy was affective as I planned what I was going to do, and I explained how I was going to do that. I got a sample from a population by using stratified sampling and put the samples in different tables. I have hand drawn one scatter graph, cumulative frequency diagram, box plot, and histogram, so that the reader understands that I know the method for my calculations. I have also done one standard deviation and Spearmans rank correlation coefficient calculation, for the same particular reason. Then I did the rest of my calculations and diagrams on Autograph, and I made a summary of each result.

Finally that had got my answers, and I could see whether my original hypotheses were right. Unfortunately one of them was wrong.

The thing I could have changed is to get both of my hypotheses right and to get my data from a real high school instead of a fictitious, however, at least the pieces data collected, were from real people which was important thing.

The things that I am proud of are that I used the correct sampling method, so that I wasn’t biased, and the sample sizes were not too small, as they were to proportion of the population.

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This student written piece of work is one of many that can be found in our GCSE IQ Correlation section.

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