# Guestimate the length and size of the angle.

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Introduction

GCSE Mathematics course work

Guestimate

1.Collect relevant data

I asked a sample of people to estimate:

- The length of this line

- The size of this angle

*Note: The data collected from this investigation is located in the Appendix of this assignment

2. Extract a sample of 30 items

I have chosen to extract two random samples of 30 people wearing spectacles and 30 people with out. The reason for this is one of hypotheses 2 involves comparing peoples estimates with spectacles and without and I wanted to make sure it is

Hypotheses 1: Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls

Hypotheses 2: People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles

Random sample of 30 people (15 boys and 15 girls) for hypothesis 1

Sample data 1:

Estimate of length of line (L) to nearest cm | Estimate of size of angle (A) to nearest degree | Age | Sex M or F | Wears spectacles | Occupation |

7 | 52 | 30 | M | No | Student |

4 | 50 | 21 | F | Yes | Student |

4 | 45 | 25 | F | No | Student |

4.5 | 45 | 23 | M | No | Student |

4.5 | 45 | 40 | M | No | Student |

2 | 45 | 25 | M | No | Student |

3 | 45 | 28 | M | No | Student |

4 | 45 | 45 | F | Yes | Lecturer |

2.5 | 45 | 12 | F | No | Student |

4 | 45 | 22 | F | No | Swimming teacher |

7 | 45 | 40 | F | No | Carer |

7 | 45 | 43 | M | No | Builder |

10 | 37 | 46 | M | No | Consultant |

4 | 40 | 22 | M | Yes | Lecturer |

3 | 45 | 21 | F | No | Network administrator |

3.5 | 45 | 20 | F | No | Assistant Manager |

3.5 | 40 | 20 | M | No | Estate Agent |

7 | 30 | 29 | M | Yes | Secretary |

6 | 60 | 32 | M | Yes | Hairdresser |

5 | 65 | 19 | F | Yes | Trainee accountant |

4.5 | 45 | 16 | M | No | Coach |

5.5 | 38 | 53 | M | Yes | Floor layer |

9 | 45 | 28 | M | No | Interior Designer |

7 | 30 | 19 | F | No | Student |

4 | 45 | 17 | F | Yes | Student |

3 | 50 | 18 | F | No | Student |

2 | 42 | 17 | F | Yes | Student |

5 | 49 | 16 | F | No | Student |

2 | 45 | 16 | F | No | Student |

3 | 62 | 18 | M | Yes | Student |

*Note:Sample data 1: is a collection

Middle

F

Student

6

45

17

M

Student

5

30

16

F

Student

6

20

19

M

Student

4

46

19

M

Student

4

43

18

M

Student

4

35

17

M

Student

6

45

16

M

Student

*Note:Sample data 3: is a collectionof data that was compiled as a result of randomly selecting data from both the data collection sheet (which I have enclosed in the Appendix)

3. Write down two hypotheses to test using your data:

- Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
- People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles

4.2 Frequency tables for Hypotheses 1

Hypotheses 1: Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls

Frequency table of estimated lengths taken from sample data 1

Estimate of length in cm | Tally | Frequency |

1 | 0 | |

2 | 111 | 3 |

2.5 | 1 | 1 |

3 | 1111 | 4 |

3.5 | 11 | 2 |

4 | 1111 1 | 6 |

4.5 | 111 | 3 |

5 | 11 | 2 |

5.5 | 1 | 1 |

6 | 1 | 1 |

6.5 | 0 | |

7 | 1111 | 5 |

7.5 | 0 | |

8 | 0 | |

8.5 | 0 | |

9 | 1 | 1 |

9.5 | 0 | |

10 | 1 | 1 |

Frequency table of estimated lengths of the Boys (15)

Estimate of length in cm | Tally | Frequency |

1 | 0 | |

2 | 1 | 1 |

2.5 | 0 | |

3 | 11 | 2 |

3.5 | 1 | 1 |

4 | 1 | 1 |

4.5 | 111 | 3 |

5 | 0 | |

5.5 | 1 | 1 |

6 | 1 | 1 |

6.5 | 0 | |

7 | 111 | 3 |

7.5 | 0 | |

8 | 0 | |

8.5 | 0 | |

9 | 1 | 1 |

9.5 | 0 | |

10 | 1 | 1 |

Frequency table of estimated lengths of the Girls (15)

Estimate of length in cm | Tally | Frequency |

1 | 0 | |

2 | 11 | 2 |

2.5 | 1 | 1 |

3 | 11 | 2 |

3.5 | 1 | 1 |

4 | 1111 | 5 |

4.5 | 0 | |

5 | 11 | 2 |

5.5 | 0 | |

6 | 0 | |

6.5 | 0 | |

7 | 11 | 2 |

7.5 | 0 | |

8 | 0 | |

8.5 | 0 | |

9 | 0 | |

9.5 | 0 | |

10 | 0 |

Selecting classes to organize data from sample data 1 (boys estimates of the angle)

The 30 estimated angles are as follows ( oC):

30, 30, 37, 38, 40, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 49, 50, 50, 52, 60, 62, 65

As the data has a range of: (65-30) = 30 I have decided to group the data into classes. A class width of 5 degrees gives 8 classes and will help to present the data in a useful way.

The class intervals are shown in the table below:

Lower class limit | Upper class limit | Class interval |

30 | 34 | 30-34 |

35 | 39 | 35-39 |

40 | 44 | 40-44 |

45 | 49 | 45-49 |

50 | 54 | 50-54 |

55 | 59 | 55-59 |

60 | 64 | 60-64 |

65 | 69 | 65-69 |

Frequency table of estimated angles taken from sample data 1

Class of estimates | Tally | frequency |

30-34 | 11 | 2 |

35-39 | 11 | 2 |

40-44 | 111 | 3 |

45-49 | 1111 1111 1111 11 | 17 |

50-54 | 111 | 3 |

55-59 | 0 | |

60-64 | 11 | 2 |

65-69 | 1 | 1 |

Frequency table of estimated angles taken from sample data 1

Class of estimates | Tally | frequency |

30-34 | 1 | 1 |

35-39 | 11 | 2 |

40-44 | 11 | 2 |

45-49 | 1111 11 | 7 |

50-54 | 1 | 1 |

55-59 | 0 | |

60-64 | 11 | 2 |

65-69 | 0 |

Frequency table of estimated angles taken from sample data 1

Class of estimates | Tally | frequency |

30-34 | 1 | 1 |

35-39 | 0 | |

40-44 | 1 | 1 |

45-49 | 1111 1111 | 10 |

50-54 | 11 | 2 |

55-59 | 0 | |

60-64 | 0 | |

65-69 | 1 | 1 |

Conclusion

= 4.55 = 5

The 30 estimated angles ( oC) are as follows (taken from sample 2 -people who wear spectacles):

30, 30, 35, 35, 37, 38, 39, 40, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 50, 50, 55, 55, 60, 62, 65, 65

The range of sample 1’s estimates of the angle = 65-30 = 30

The Median angle = =45+45 / 2 =45

The Mode angle = 45

The Mean = cumulative estimates (1303) divided by total number of estimates (30)

= 43.43 = 43

The 30 estimated angles ( oC) are as follows (taken from sample 3-people who do not wear spectacles):

20, 26, 30, 30, 35, 40, 43, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 49, 50, 52, 55

The range of sample 1’s estimates of the angle = 55-20 = 35

The Median angle = =45+45 / 2 =45

The Mode angle = 45

The Mean = cumulative estimates (1286) divided by total number of estimates (30)

= 42.86 = 43

6.2 Pie charts

These pie charts, which are not drawn to scale, show the distribution of estimates by people who part of the investigation.

Pie chart representing percentages of 30 people’s (wearing spectacles) estimates of the length

*Note:Any estimates with a value of zero are not represented in this chart

The mode estimate for the both these pie charts are represented by the largest portion

Pie chart representing percentages of 30 people’s ( not wearing spectacles) estimates of the length

Pie chart representing percentages of 30 people’s (wearing spectacles) estimates of the Angle

*Note:The mode estimate for the both these pie charts are represented by the largest portion

Pie chart representing percentages of 30 people’s (not wearing spectacles) estimates of the angle

This frequency diagram shows the distribution of estimates of the length

This frequency diagram shows the distribution of estimates of the angle

Handling data: Created by Joel Mahatsri

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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