# My hypothesis is to see if there is a difference between two ages estimating angle and length is different. I also think that people are better at estimating lengths than angles.

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Introduction

## Maths coursework 2001 Oliver Goddard

## My hypothesis’s

My hypothesis is to see if there is a difference between two ages estimating angle and length is different. I also think that people are better at estimating lengths than angles.

Also to see if males are better than females at estimating the length and angle.

And if playing sport helps at estimating lengths and angles.

I think that the older people are better at estimating angles and the length because they have more experience at doing so from further education and more experience.

I also think that the male sex will be better at estimating this better than the female sex because they play more sport and have to judge lengths and angles more of the time e.g. football, basketball, rugby.

I have done a pre test to make sure that my main experiment will work by cheeking the method and data collection sheet

For all three of my experiments the length of the line and the degrees of the angle will be the same the length will be 4.5 centimetres and the degrees of the angle will be 36 degrees

## Plan

#### I will collect data from year 7 and year 11 boys and girls

To make sure it will be a fair test by making sure the subjects have the same amount of time to estimate the length of the line and the degrees of the angle.

Middle

7

8

8

40

0

0

2

2

8

50

6

60

0

1

3

4

70

2

Female

##### Angle

Mean 1152 / 30 = 38.4

## Median 34 the median is close to the original angle of 36

Mode 30 this means that most females are closer to the originalangle

Range 57

##### The median is close to the actual angle

Female | Length | ||||||||

3 | 0 | 0 | |||||||

4 | 0 | 0 | 0 | 0 | 0 | ||||

5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 |

6 | 0 | 0 | 0 | 0 | 0 | ||||

7 | 0 | 0 | |||||||

8 | 0 | 0 | 0 | 0 | |||||

9 | 0 | 0 | |||||||

10 | 0 |

##### Length

Mean 175.4 / 30 = 5.846666667

Median 5 close to 4.5 cm

Mode 5

Range 70

###### Most females are closer than the males to 4.5 cm plus one female estimated the angle to be 4.5 which was correct

Cumulative frequency and Box and whisker graphs

Angle | Frequency | Cum.Freq |

10 to 19 | 2 | 2 |

20 to 29 | 4 | 6 |

30 to 39 | 13 | 19 |

40 to 49 | 5 | 24 |

50 to 59 | 1 | 25 |

60 to 69 | 4 | 29 |

70 to 79 | 1 | 30 |

Length | Frequency | cum.freq |

3 to 3.9 | 2 | 2 |

4 to 4.9 | 5 | 7 |

5 to 5.9 | 9 | 16 |

6 to 6.9 | 5 | 21 |

7 to 7.9 | 2 | 23 |

8 to 8.9 | 4 | 27 |

9 to 9.9 | 2 | 29 |

10 to 10.9 | 1 | 30 |

Male

Stem and leaf

Male | Angle | |||||||||

10 | 5 | 9 | ||||||||

20 | 0 | 1 | 6 | 7 | 8 | 8 | ||||

30 | 0 | 0 | 2 | 2 | 4 | 5 | 7 | 7 | 8 | 9 |

40 | 0 | 1 | 1 | 2 | 8 | |||||

50 | ||||||||||

60 | 0 | 0 | 1 | 3 | ||||||

70 | 2 | |||||||||

80 | 1 |

This stem and leaf counts to 29 this is a mistake but dose not affect my results

Angle

Mean 1167 / 30 = 38.9 (1167 / 29 = 40.24137931)

## Median 37

Mode 37 the male majority are closer than the females on angles

Range 66

###### The mode and the median are the same meaning that the 15th male was also in the median

Male | Length | ||||||

2 | 0 | ||||||

3 | 0 | 0 | |||||

4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | 0 | 5 | |

6 | 0 | 0 | |||||

7 | 0 | ||||||

8 | 0 | 0 | 0 | 0 | 0 | 4 | |

9 | 0 | 0 | |||||

10 | 0 | ||||||

11 | |||||||

12 | 0 | ||||||

13 | |||||||

14 | |||||||

15 | |||||||

16 | 0 |

Huge range no males got the angle right

##### Length

Mean 189.9 /30 = 6.33

Median 5 very close to the original angle of 4.5 cm

Mode 4 the median is also the same as the females median

Range 14

The range for the males is bigger than the females because there are a couple of males that estimated a lot higher than I would expected

Cumulative frequency and Box and whisker graphs

Angle | Frequency | Cum.freq |

10 to 19 | 2 | 2 |

20 to 29 | 6 | 8 |

30 to 39 | 10 | 18 |

40 to 49 | 5 | 23 |

50 to 59 | 0 | 23 |

60 to 69 | 4 | 27 |

70 to 79 | 1 | 28 |

80 to 89 | 1 | 29 |

Length | Frequency | cum.freq |

2 to 2.9 | 1 | 1 |

3 to 3.9 | 2 | 3 |

4 to 4.9 | 7 | 10 |

5 to 5.9 | 6 | 16 |

6 to 6.9 | 2 | 18 |

7 to 7.9 | 1 | 19 |

8 to 8.9 | 6 | 25 |

9 to 9.9 | 2 | 27 |

10 to 10.9 | 1 | 28 |

11 to 11.9 | 0 | 28 |

12 to 12.9 | 1 | 29 |

13 to 13.9 | 0 | 29 |

14 to 14.9 | 0 | 29 |

15 to 15.9 | 0 | 29 |

16 to 16.9 | 1 | 30 |

Conclusion

Males are better at estimating lent as the box and whisker graphs prove though the males have a very big range most of the males have been close to the 4.5 cm chosen

An experiment to see if playing sport helps at estimating lengths and angles

This is a test including only 10 people that play sport and 10 people that don’t

In this test sex is not important as it is only comparing non-players against players

The players and non-players have been chosen at random from a group of 60 people.

Here are the results:

Angle | Length | Angle | Length | |||

20 | 8 | Y | 1 | 64 | 5 | N |

27 | 10 | Y | 2 | 38 | 7 | N |

32 | 5 | Y | 3 | 15 | 6 | N |

41 | 3 | Y | 4 | 61 | 10 | N |

50 | 8 | Y | 5 | 60 | 9 | N |

35 | 2 | Y | 6 | 30 | 8 | N |

40 | 5 | Y | 7 | 30 | 4 | N |

32 | 7 | Y | 8 | 35 | 4 | N |

26 | 6 | Y | 9 | 39 | 4 | N |

34 | 8.4 | Y | 10 | 30 | 5 | N |

337 | 62.4 | 402 | 62 |

I could improve my sample by having a wider range of subjects to chose from and also have a bigger sample.

Non-players

Length | |||

4 | 0 | 0 | 0 |

5 | 0 | 0 | |

6 | 0 | ||

7 | 0 | ||

8 | 0 | ||

9 | 0 | ||

10 | 0 |

Mean 62 / 10 =6.2

Median 5

Mode 4

Range 6

###### You can see that the non-players have

Angle | ||||||

10 | 5 | |||||

20 | 0 | 0 | 0 | 5 | 8 | 9 |

30 | ||||||

40 | ||||||

50 | ||||||

60 | 0 | 1 | 4 |

Mean 402 / 10 =40.2

Median 25

Mode 20

##### Range 49

###### Most of the non players have there angle marked between

Cumulative frequency and Box and whisker graph

Length | Frequency | cum.freq |

4 to 4.9 | 3 | 3 |

5 to 5.9 | 2 | 5 |

6 to 6.9 | 1 | 6 |

7 to 7.9 | 1 | 7 |

8 to 8.9 | 1 | 8 |

9 to 9.9 | 1 | 9 |

10 to 10.9 | 1 | 10 |

Angle | Frequency | Cum.Freq |

10 to 19 | 1 | 1 |

20 to 29 | 6 | 7 |

30 to 39 | 0 | 7 |

40 to 49 | 0 | 7 |

50 to 59 | 0 | 7 |

60 to 69 | 3 | 10 |

Conclusion

I think that the older people are better at estimating angles and the length because they have more experience at doing so from further education and more experience.

For this experiment I am using excel again as it it’s a time saving device and also Is a excellent calculator at fast speed if you know the formula to put in for this experiment and all of these experiments I have used the =SUM formula the most. Year 10s chosen underlined in red:

Year 7 | Year 10 | |||

Angle | Length | Angle | Length | |

60 | 5 | 1 | 30 | 3.5 |

15 | 8 | 2 | 30 | 5 |

20 | 8 | 3 | 40 | 4.8 |

27 | 10 | 4 | 30 | 5 |

32 | 5 | 5 | 40 | 4.5 |

41 | 3 | 6 | 30 | 5 |

81 | 8 | 7 | 20 | 4 |

28 | 4 | 8 | 40 | 5 |

30 | 4 | 9 | 35 | 5 |

35 | 4 | 10 | 58 | 5 |

39 | 4 | 11 | 45 | 4.5 |

21 | 5 | 12 | 45 | 5 |

28 | 8 | 13 | 50 | 4 |

32 | 7 | 14 | 45 | 5 |

26 | 6 | 15 | 25 | 4 |

15 | 6 | 16 | 30 | 4 |

61 | 10 | 17 | 45 | 5 |

60 | 9 | 18 | 40 | 5 |

30 | 8 | 19 | 30 | 6 |

30 | 7 | 20 | 30 | 6 |

32 | 5 | 21 | 40 | 4.5 |

30 | 6 | 22 | 45 | 2.5 |

48 | 8 | 23 | 20 | 3 |

56 | 4 | 24 | 45 | 3 |

72 | 4 | 25 | 45 | 3 |

31 | 6 | 26 | 45 | 3.5 |

34 | 8 | 27 | 45 | 4 |

30 | 3 | 28 | 45 | 4 |

38 | 9 | 29 | 45 | 4 |

42 | 4 | 30 | 40 | 4 |

1124 | 186 | TOTAL | 1153 | 130.8 |

I could of hade made my sample bigger but that would had of taken more time and also a sample of 30 is easier to work with.

## Year 7

##### Stem and leaf diagrams

##### Angles

Angle | |||||||||||||

Year 7 | |||||||||||||

10 | 5 | 5 | |||||||||||

20 | 0 | 1 | 6 | 7 | 8 | 8 | |||||||

30 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 2 | 4 | 5 | 8 | 9 |

40 | 1 | 2 | 8 | ||||||||||

50 | 6 | ||||||||||||

60 | 0 | 0 | 1 | ||||||||||

70 | 2 | ||||||||||||

80 | 1 |

Mean 1124 / 30 = 37.5

Median 32

Mode 30

Range 70

The year 7s are closer to the angle

Length

Length | |||||||

3 | 0 | 0 | |||||

4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | |||

6 | 0 | 0 | 0 | 0 | |||

7 | 0 | 0 | |||||

8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 0 | 0 | |||||

10 | 0 | 0 |

Mean 186 / 30 = 6.2

Median 6

Mode 4/8 there are two even modes for this graph as four and eight

Range 7 have the same amount on the graph so I put both of them down

Cumulative frequency and Box and whisker graphs

Year 7 | ||

Angle | Frequency | cum.freq |

10 to 19 | 2 | 2 |

20 to 29 | 6 | 8 |

30 to 39 | 13 | 21 |

40 to 49 | 3 | 24 |

50 to 59 | 1 | 25 |

60 to 69 | 3 | 28 |

70 to 79 | 1 | 29 |

80 to 89 | 1 | 30 |

Length | Frequency | cum.freq |

3 to 3.9 | 2 | 2 |

4 to 4.9 | 7 | 9 |

5 to 5.9 | 4 | 13 |

6 to 6.9 | 4 | 17 |

7 to 7.9 | 2 | 19 |

8 to 8.9 | 7 | 26 |

9 to 9.9 | 2 | 28 |

10 to 10.9 | 2 | 30 |

Year 10

Stem and leaf diagrams

##### Angles

Angle | |||||||||||||||||

Year 10 | |||||||||||||||||

20 | 0 | 0 | 5 | ||||||||||||||

30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | |||||||||

40 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

50 | 0 | 8 |

Mean 1153 / 30 =38.4

Median 40

Mode 45

###### Range 38

Length

Length | ||||||||||||

2 | 5 | |||||||||||

3 | 0 | 0 | 0 | 5 | 5 | |||||||

4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 5 | 5 | 8 |

5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||

6 | 0 | 0 |

## Mean 130.8 / 30 = 4.3

## Median 4.5

Mode 5

Range 3.5

Cumulative frequency and Box and whisker graphs

Year 10 | ||

Angle | Frequency | cum.freq |

20 to 29 | 3 | 3 |

30 to 39 | 8 | 11 |

40 to 49 | 17 | 28 |

50 to 59 | 2 | 30 |

Length | Frequency | cum.freq |

2 to 2.9 | 1 | 1 |

3 to 3.9 | 5 | 6 |

4 to 4.9 | 12 | 18 |

5 to 5.9 | 10 | 28 |

6 to 6.9 | 2 | 30 |

Conclusion

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