# Maths Coursework - Statistics Mayfield High School

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Introduction

Sonal Halai 11Q

Maths Coursework – Statistics

Mayfield High School

Introduction

My investigation will be based on information from Mayfield High School, a fictitious school. I will use a wide range of mathematical techniques to present my data and findings in different ways. I will explore two different hypotheses for this piece of coursework.

## Hypothesis 1

I believe that ‘Girls are more intelligent than boys’. I predict that this investigation will prove that girls are more intelligent than boys. There are plenty of surveys that show that key stage 2 results are higher for girls than boys. With this hypothesis I will also investigate whether ‘IQ results are directly proportional to Key Stage 2 results’. I believe that as the IQ result increases the Key Stage 2 result will also increase.

## Plan

By comparing the differences between two factors, for girls and boys, I will be able to determine which gender is more intelligent. The two factors I will compare are IQ results and Key Stage 2 results.

I will be using a random sample of 100 students - 50 boys and 50 girls. These 100 students will be selected randomly from year 7. I will then use this sample to analyse the information and make judgements about it. I will make graphs and charts to show my results, which I will use to draw my conclusions on my information.

Middle

Mark (m)

M < 2

M < 3

M < 4

M < 5

M < 6

Cumulative frequency

0

8

34

50

50

For the boys' Key stage 2 results, you can see from the curve that all three subjects are very close in the results that the students achieved. All three subjects had the same average level for the boys.

As you can see from the cumulative frequency table of results, most of the boys achieved a level 4 in all three subjects, which shows that the majority of boys do not excel in one particular subject.

The following table shows the chart with which I worked out class widths and frequencies for the histogram that shows the results for the boys' IQ.

Class interval | Class width | Frequency | Frequency density |

70 < m < 90 | 20 | 2 | 0.1 |

90 < m < 105 | 15 | 33 | 2.2 |

105 < m < 110 | 5 | 10 | 2 |

110 < m < 120 | 10 | 5 | 0.5 |

I decided to use these class intervals for the construction of this histogram because they are most appropriate. The first class width started at 70 because from the information that I had gathered it did not show that any boys were achieving below this mark in their IQ. As there are not many people who were getting between 70 and 80 for their IQ results, I decided to make the interval slightly wider to 70 - 90 points. I used the next interval because there were a few people who would be put into this interval. I thought it best to have one overall interval that held the majority of students. I chose a small interval again for the next two because it seemed that they did not contain many students.

The average IQ result for the boys was 99.

The next thing I did was to find the average for the Girls' Key stage 2 results. Here is what I found:

English

5 + 5 + 5 + 5 + 5 + 5 + 4 + 4 + 4 + 4 + 5 + 4 + 4 + 5 + 4 + 4 + 3 + 3 + 4 + 3 + 5 + 5 + 4 + 5 + 4 + 4 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 4 + 5 + 3 + 5 + 4 + 4 + 5 + 3 + 5 + 5 + 5 + 5 + 4 + 5 + 5 + 5 + 4 = 215

215 = 4.3

50

Mean average girls' English result is level 4

Maths

6 + 4 + 5 + 5 + 4 + 5 + 4 + 4 + 4 + 4 + 5 + 4 + 3 + 5 + 4 + 4 + 3 + 3 + 4 + 3 + 5 + 5 + 4 + 5 + 4 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 3 + 4 + 4 + 4 + 5 + 3 + 5 + 4 + 5 + 4 + 5 + 5 + 5 + 5 + 4 = 210

209 = 4.2

50

Mean average girls' Maths result is level 4

Science

5 + 5 + 5 + 5 + 4 + 5 + 4 + 4 + 4 + 4 + 6 + 4 + 4 + 5 + 5 + 4 + 3 + 4 + 5 + 3 + 4 + 5 + 4 + 5 + 4 + 4 + 3 + 4 + 4 + 5 + 5 + 4 + 4 + 5 + 5 + 4 + 4 + 5 + 4 + 5 + 3 + 5 + 5 + 5 + 4 + 5 + 5 + 5 + 6 + 5 = 223

223 = 4.56

50

Mean average girls' Science results is level 5

However, although the mean averages for the girls' results say that the majority of girls are achieving level 4 in their key stage 2 results, if you compare this with the mode averages, then I get slightly different results.

The mode averages suggest that the majority of girls are achieving level 5 in their key stage 2 exams. (Excluding the maths results with which the average would still be level 4). The following tables show this:

Percentage and cumulative frequency tables for the girls' Key stage 2 Results

## English

Mark ( M ) | 2 | 3 | 4 | 5 | 6 |

Frequency | 0 | 7 | 21 | 22 | 0 |

Mark (m) | M < 2 | M < 3 | M < 4 | M < 5 | M < 6 |

Cumulative frequency | 0 | 7 | 28 | 50 | 50 |

## Maths

Mark (m) | 2 | 3 | 4 | 5 | 6 |

Frequency | 0 | 9 | 23 | 17 | 1 |

Mark (m) | M < 2 | M < 3 | M < 4 | M < 5 | M < 6 |

Cumulative frequency | 0 | 9 | 32 | 49 | 50 |

Conclusion

My results are not completely accurate due to the fact that I have rounded most of my figure to give an integer this means that my results are slightly wrong. Also when sampling I could have been biased and chosen the data to suit me this would mean that my results are not as precise as they should be. There are many factors which could slightly jeopardise my results such as there could have been a type error the list could go on.

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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