# What factors made a person better at estimating the size of an angle or the length of a line.

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Introduction

Michael Mitchell Statistics Coursework Mrs Williams

From this data we made a hypothesis on what factors made a person better at estimating the size of an angle or the length of a line. My hypothesis was that year 10 pupils would be better at estimating both the size of angles and the length of lines than the adults and the year 7 children but adults answers will be closer to the mean on average. To prove this I would have to use the information in the spreadsheet .

I first found the mean of angle 1 ,angle2 ,line 1 and line 2 in all of the sample of year ten all of the sample of year seven and all of the sample of the adults because using this I could find the average percentage error of each group because I felt this was essential in trying to prove the hypothesis I made earlier .The means for each were as displayed in the table below:

Year 10 | Year 7 | Adults | |

Angle1 | 57.76 | 65.42 | 51.25 |

Angle 2 | 142.72 | 141.04 | 147.05 |

Line 1 | 3.87 | 4.55 | 3.6275 |

Line 2 | 14.52 | 14.61 | 12.7325 |

At the moment when I produced

Middle

Year 7 | Upper Fence | Lower fence |

Angle 1 | 92.5 | 32.5 |

Angle 2 | 205 | 85 |

Line 1 | 7.25 | 1.25 |

Line 2 | 19.5 | 7.5 |

And for the adults

Adults | Upper Fence | Lower fence |

Angle 1 | 65 | 33 |

Angle 2 | 188.75 | 110.75 |

Line 1 | 5.5 | 1.625 |

Line 2 | 6.875 | 17.675 |

With this data we deleted rogue values which amounted only to three.

So now we can find the percentage error without worrying about rogue values influencing what could be a vital difference.

Year 10 (%) | Year 7 (%) | Adults (%) | |

Angle 1 | 7.2 | 18.9 | 6.8 |

Angle 2 | 7.9 | 9.03 | 5.12 |

Line 1 | 4.6 | 23 | 2 |

Line 2 | 16.17 | 16.88 | 1.9 |

This gives us an idea of to which group is better at estimating the sizes of angles and the lengths of lines but to see this in another way we can use box plots which are very useful for comparing sets of data from different groups within a certain population. The length of the whiskers

Conclusion

If I could reiterate the experiment I would make a more detailed hypothesis inducing me to analyse all possible fields that could of affected a persons ability to estimate the size of angles and lengths of lines an example of this is gender or intelligence but the field that I investigated which was age came out to me with a very clear result , this was that on average the older you are the better you are at estimating the size of an angle and the length of a line ,but we must take into account that we used a random sample of 25% from each group this meant that we could of missed some peoples estimates that could of affected or swayed the results to a different conclusion this could be important. This means the concluding statement may not actually be correct if further investigated with more detail and with more age groups such as year 8 , 9 and 11 but is still correct for the investigation we carried out.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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