# Aim: having been presented with some data, to come up with a hypothesis and try to prove or disprove it using statistical techniques

Extracts from this document...

Introduction

Mayur Gohel 11 BEM

GCSE Maths coursework

ContentsPage number

Section One

Introduction1

15% error margin for the line 4

15% error margin for the angle 5

Scatter diagrams 6

Section Two

Organisation and analysis of data for 7

the length of the line

Organisation and analysis of the data for 8

the size of the angle

Organisation and analysis of diagrams 9

Pie charts 10

Conclusion 11

Aim: having been presented with some data, to come up with a hypothesis and try to prove or disprove it using statistical techniques

Eighty six year eleven students from my school were presented with a sheet of paper with a line drawn and an angle drawn on it. They were told without using any measuring equipment to estimate how long the line was in centimetres within 30 seconds, as well as having to find out the size of the angle in degrees without using measuring equipment and within a 30 second time limit. Having been handed with the results of these students, I have created a hypothesis that I want to investigate, this is to find out if 75% of students got within 15% of the line and 15% of the angle.

I wish to investigate this further amongst 30 students, as I feel that this will allow me to get an idea of how the whole group would have reacted to this. The reason I have chosen 30 is because I personally feel this is a sample size which allows me to have a balanced selection.

Middle

86

3.2

50

Actual result: Length: 7.9 cm Angle: 34 degrees

Glancing upon my sample I have noticed two anomalies, in reference numbers 29 and 69, occurring in the length part of the table. Number 29 states that the person thinks the line is of a length of “73.0” and number 69 thinks that the length of the line is “0.7.” These values are completely inaccurate with regards to the genuine 7.9 length, possibly the student decided upon the wrong units of length and therefore the answers they came up with were wrong. Acknowledging this, I have decided to discard those values and instead pick two more values still using random sampling.

The values I now got were:

Reference | Length | Angle |

36 | 8.2 | 42 |

54 | 5.5 | 40 |

Section One:

Finding the margin of error for the length of the line

In this section of the investigation I hope to explain to you what error margin means with regards to the length of the line and what the boundaries should be, in which I have to stick to in order to agree with the hypothesis.

Firstly I will need to find out what the 15% error margin is for line. In order to do this I will use the accurate figure of 7.9 (centimetres) which I found out for the line by measuring it with a ruler. I shall now work out what the error margin above the length of the line is; initially I will do this calculation ‘115/100 x 7.9’ to which the answer is 9.

Conclusion

No

3.2

No

Section two

Organisation and analysis of the data for the size of the angle

Estimations of the size of the angle | Does it comply with the hypothesis? |

40 | No |

40 | No |

35 | Yes |

35 | Yes |

40 | No |

30 | Yes |

30 | Yes |

50 | No |

35 | Yes |

41 | No |

36 | Yes |

38 | Yes |

42 | No |

32 | Yes |

37 | Yes |

39 | Yes |

26 | No |

40 | No |

39 | Yes |

40 | No |

40 | No |

39 | Yes |

36 | Yes |

35 | Yes |

44 | No |

40 | No |

39 | Yes |

39 | Yes |

29 | Yes |

50 | No |

These pie charts show that 57% of people estimated the line and the angle incorrectly.

However my hypothesis states that those who get within the 15 % of the line will also get within 15 % of the angle, so therefore I am going to create a table which has the figures of those who got within 15% of the line.

It is within the boundaries of the length of the line | Is it within the boundaries for the angle? | Does this comply with the hypothesis? |

9.0 | No | No |

7.5 | Yes | Yes |

8.0 | Yes | Yes |

7.0 | Yes | Yes |

8.0 | Yes | Yes |

8.0 | No | No |

8.2 | No | No |

7.5 | Yes | Yes |

8.2 | No | No |

7.8 | Yes | Yes |

7.2 | Yes | Yes |

8.6 | Yes | Yes |

7.1 | No | No |

7.5 | No | No |

8.6 | Yes | Yes |

8.2 | Yes | Yes |

6.8 | Yes | Yes |

From this I understand that 11 out of a possible 17 comply with the hypothesis, this as a percentage gives me 64.70…, and therefore I have decided to round it to the nearest whole number, which gives me 65%.

In my hypothesis I thought that 75% of people who got within the boundaries of the line would also get within the boundaries of the angle however this was not true, as 13 of the 17 people would have had to have got within both the 15% boundaries.

Therefore my hypothesis was incorrect.

This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.

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