# Maths Statistics Coursework - Mayfield School Data

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Introduction

Maths Statistics Coursework – Mayfield School Data

## Louise Bishop

### 5A

Task Description and Specifying the problem and Plan.

Specify and discuss the Hypotheses

I will investigate the following statements. I was interested in how age would affect a number of factors and so I chose to investigate the age variable. I decided to investigate the following hypotheses:

- How does age affect height? You get taller as you get older
- How does age affect weight? You get heavier as you get older.
- How does age affect IQ? You get more intelligent as you get older.

I hope to be able to draw firm conclusions from these three hypotheses. I will also be interested to see the conclusions to the third hypotheses to see if you get more intelligent with age. As I thought about this, I realised that there is a subtle difference between IQ and exam results and so I decided to investigate an extra hypotheses.

- How does IQ affect exam results? A high IQ guarantees good exam performance.

I think this statement will be particularly interesting as I do not think that intelligence would necessarily suggest a good exam result. People with a very high IQ may well expect to get good exam results, but would this trend be consistent? My final hypothesis is to investigate the merits of a high or low IQ.

- Does a high IQ suggest strength in a particular subject? People with a high IQ tend to be mathematicians or at least score well in mathematics.

This will be an interesting hypothesis to investigate. I am not sure how I will investigate it at this stage but I hope to have formulated some ideas when it comes to processing the data when analysing this hypotheses.

I will use numerical methods to analyse the data as well as graphical.

Middle

Tables constructed to form a cumulative frequency curve for height

Height (m) | Tally | Frequency |

1.20<x≤1.35 | II | 2 |

1.35<x≤1.45 | IIIII | 5 |

1.45<x≤1.55 | IIIII IIIII IIIII | 15 |

1.55<x≤1.65 | IIIII IIIII IIIII IIIII | 20 |

1.65<x≤1.75 | IIIII IIIII III | 13 |

1.75<x≤1.85 | IIIII | 5 |

Height (m) | Frequency | Cumulative Frequency | UCB |

1.20<x≤1.35 | 2 | 2 | 1.35 |

1.35<x≤1.45 | 5 | 7 | 1.45 |

1.45<x≤1.55 | 15 | 22 | 1.55 |

1.55<x≤1.65 | 20 | 42 | 1.65 |

1.65<x≤1.75 | 13 | 55 | 1.75 |

1.75<x≤1.85 | 5 | 60 | 1.85 |

#### Tables constructed to form a cumulative frequency curve for weight

Weight (Kg) | Tally | Frequency |

0<x≤33 | I | 1 |

33<x≤41 | IIIII I | 6 |

41<x≤49 | IIIII IIIII IIIII IIIII IIIII IIIII | 25 |

49<x≤57 | IIIII IIIII IIIII III | 18 |

57<x≤65 | IIIII II | 7 |

65<x≤73 | III | 3 |

Weight (Kg) | Frequency | Cumulative Frequency | UCB |

0<x≤33 | 1 | 1 | 33 |

33<x≤41 | 6 | 7 | 41 |

41<x≤49 | 25 | 32 | 49 |

49<x≤57 | 18 | 50 | 57 |

57<x≤65 | 7 | 57 | 65 |

65<x≤73 | 3 | 60 | 73 |

#### Once I had drawn the cumulative frequency curves, I worked out the median, Inter-quartile range (IQR), the modal class and the mean (from the grouped frequency table above) for both distributions (height and weight). All the working is shown above.

I performed all of these calculations so I could easily compare the two separate distributions of height and weight.

By looking at the shape of the curves, I can see instantly an important difference in the spread of the two distributions. The height graph has a much larger spread, indicating variation from the mean, whereas the weight graph has much less deviation from the mean. This means that the people in my sample are much closer related by weight than by height. This is indicated on the gradient of the lines. The weight curve has a much larger gradient throughout and is more ‘direct’ than the height graph. This suggests little standard deviation. However, the height graph has a much more wallowing gradient which indicates greater deviation from the mean and therefore a greater spread and range.

This relationship is also shown by the IQRs.

Conclusion

I think that some of the conclusions that I have discovered are significant to the real world. For example the findings about height variation increasing with age would be very significant to a school shop ordering trousers or jackets. Based on my fin dings they would need to order a greater range of sizes for Year 11 than they would for Year 7.

To extend this project, I would like to focus on my last conclusion. I would like more detailed data than just SATS levels. I would like to have data on employment figures for schoolchildren for deeper analysis into this last idea. E.g. individual percentage marks for GCSE results, ideal career choice, eventual career, OASIS test results etc.

I think that the project went well, but next time I would reduce the amount of work I had to do as I spent too much time working on the project. To do this, I would focus on just one or two hypothesis in the next project. Despite this, I think that the project went smoothly and I was able to make inferences linking back to every hypothesis, which is pleasing. I also think that the conclusions that I made are accurate and reliable and are significant to the real world. I think that the project was a success, but next time I would have fewer hypotheses. This would enable me to go into further detail to form more detailed conclusions. I would also take a larger sample to make the conclusions more reliable. Overall the investigation was a success because I was able to make valid and reliable conclusions and come to a judgement on every one of my hypotheses.

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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