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Guestimate the length and size of the angle.

Extracts from this document...

Introduction

GCSE Mathematics course work

Guestimate

1.Collect relevant data

I asked a sample of people to estimate:

image00.pngimage00.png

  • The length of this line image08.png

image16.png

  • The size of this angleimage19.png

*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

...read more.

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:

  1. Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
  2. 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   1image21.png

6

4.5

111

3

5

11

2

5.5

1

1

6

1

1

6.5

0

7

1111image27.png

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

1111image01.png

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

111image01.pngimage01.pngimage01.png

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

11image01.png

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

1image01.pngimage01.png

1

45-49

1111  1111  

10

50-54

11

2

55-59

0

60-64

0

65-69

1

1

...read more.

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

image05.pngimage12.pngimage15.pngimage02.png

image36.png
*Note:Any estimates with a value of zero are not represented in this chartimage09.pngimage06.pngimage20.pngimage10.pngimage07.pngimage11.pngimage22.png

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

image37.pngimage05.pngimage26.pngimage12.pngimage06.pngimage24.pngimage23.pngimage13.pngimage25.pngimage14.pngimage10.png

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

image38.png

*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

image37.png


This frequency diagram shows the distribution of estimates of the length

image30.png

This frequency diagram shows the distribution of estimates of the angle

image31.png



Handling data:                                                                               Created by Joel Mahatsri

...read more.

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