• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15

Investigate people's judgement of measurements.

Extracts from this document...

Introduction

Nathan Hart        Maths Coursework        22 FEB 2003

Statistics Coursework:

Judgement of

Distance

By Nathan Hart


Judgement of Measurements

Object

I have decided to investigate people’s judgement of measurements as the subject for my Statistics Coursework.

Before starting this experiment I needed to define guidelines that would establish the fairness of the tests method of assessment. The method I chose to fulfil this requirement was to:

  1. Place the test candidates at one end of a table with their eyes level with the table-top
  2. Ask the candidates to look horizontally across the table at a pin located at a fixed position in the middle of a sheet of graph-paper [see diagram 1].
  3. Require the candidate to mark (on the graph-paper) that distance where they thought the pin was located (firstly marking using their right hand, and then their left). Viewing, per hand, is firstly using both eyes followed by each eye individually, right first.  The difference between the estimated and the actual position of the target pin is measured for each of the eye conditions. These 3 results are added together to give the final result.

This method creates two problems:

  1. How the candidate should mark the point which they feel is in line with the pin. I have chosen to use a pin as a marker since I feel it both represents the object they were viewing and gives a greater degree of accuracy than a pencil mark.
  2. How far to the side from the target pin should the candidate mark the graph-paper.
...read more.

Middle

3

2

17

8

12

6

15

10.5

13

15

26

15

12

6

11

22

* Denotes anomalous results which have been disregarded for the purposes of the graph, table totals and averages. This was thought a result of ‘seeing’ the target between tests with and without glasses on.

22

23

21

8

131*

8*

13.5

18.5

44

14

3

9

3

9

20

9

16

20

5

5

TOTAL:

344.5

410.5

MEAN:

11.9

14.2

Sample 3

Data: Girls judgement compared with that of Boys

To test whether girls are better judges of distance than boys I will compare every fifth boy and girl results when using their favoured hand. Candidates must not be spectacle wearers, as we would then be introducing another variable. The data shown is the total score of the candidates three estimates using their preferred hand.

Table5   Distance judgement by Girls compared with Boys (Sum of estimates mm)

Boys

Girls

52

81

21

44

13

14

29

6

33

9

19

5

19

20

16

4

22

12

18

50

11

19

20

5

39.5

40

6.5

14

27

6.5

20

16

40

16

20

11

0

11

53

5

1

4

6

12

4

17

76

40

18

3

5

12

59

13

4

11

28

8

27

20

TOTAL:

707

528.5

MEAN:

23.6

17.6


The data from table 5 has been grouped here into a second table 6. The reason for me doing this is so that I am able to then transfer the data in table 6, firstly into a frequency density graph, and then cumulative frequency graphs from table 7.

Table 6  Boys vs Girls grouped into 10mm increments

Mm

Boys(f)

Girls(f)

x (midpoint)

Boys(fx)

Girls(fx)

0 – 10

7

10

5

35

50

-20

10

15

15

150

225

-30

6

0

25

150

0

-40

3

2

35

105

70

-50

0

2

45

0

90

-60

3

0

55

165

0

-70

0

0

65

0

0

-80

1

0

75

75

0

-90

0

1

85

0

85

Sum fx

30

30

∑ fx

680

520

Table 7  Cumulative frequency

mm

Boys Cf

Girls Cf

0 – 10

7

10

0 – 20

17

25

0 – 30

23

25

0 – 40

26

27

0 – 50

26

29

0 – 60

29

29

0 – 70

29

29

0 – 80

30

29

0 – 90

30

30

Cf – Cumulative frequency


Conclusions for Sample 1

  1. Whether the individual is right or left handed

For this sample I predicted that handedness will have no effect on judgement of distance.

I made this prediction because the hands have nothing to do with a candidate’s judgement of distance, it is their eyes. As you can see from my results this apparently is the case.

...read more.

Conclusion

The tests I applied examined:

  • Firstly, the effect of an individuals handedness. My measurements, including a repeat second test, when analysed by tables of comparison, stem and leaf and box and whisker diagrams confirmed my prediction 1. There is no conclusive difference dependant on handedness. There was however considerable individual variability between candidates confirming my hypothesis that estimation of distance is an individual attribute.
  • Secondly, estimates of distance by candidates requiring spectacles would be better when wearing their spectacles than when not. My measurements did indicate estimation of distance was better when wearing their spectacles. A line of best fit from a scatter graph supported this conclusion although again there was considerable variation of estimates.
  • Thirdly, that girls would be better than boys at estimating distances. My measurements, including a second test, clearly supported this conclusion. The results were probably the most conclusive of all the tests. Superimposed graphs of the two tests for the Boys and Girls showed very good reproducibility of these results although individual estimates varied widely in both groups. However the Boys showed the greatest variation further supporting the conclusion that, on average, girls are better at estimating distance.

Whilst the indications are all my predictions have been shown to be apparently correct, the degree of variability from individual results makes absolute conclusions difficult. In any extension of the work I would try and increase the size of the test population database. This would increase the confidence in the conclusions.

Page  of

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Statistics coursework

    4 13 11 Female 117 5 5 5 15 11 Female 106 5 4 5 14 11 Female 101 5 5 5 15 11 Female 104 4 4 5 13 11 Female 110 5 5 5 15 11 Female 95 4 3 4 11 11 Female 104 4 4 4

  2. Intermediate Maths Driving Test Coursework

    Here we see a very negative correlation with only about one or two anomalies, around four points lie on the line of best fit. It is steep indicating that instructor C is a good teacher. Here we see a strong negative correlation, which is very steep, I think Instructor C is good at teaching males.

  1. Probability of Poker Hands

    for the five cards and therefore, we must eliminate the possibility of getting the straight with the same suite. There are 40 ways of getting a straight flush. Choosing a Flush (all cards from the same suit): The possibility of getting a flush can be represented by 4C1 x 13C5.

  2. I am going to design and then carry out an experiment to test people's ...

    23 21.5 17 21 18.5 8 24 21 24 19 24 8 25 19 17 16 17 8 26 16.5 16.5 17 21 8 27 13

  1. Study of the height/diameter ratio of limpets inhabiting the middle shore region of exposed ...

    In reality, not all limpets will be able to find the ideal microhabitat. To deal with harsher conditions, the only way to cope would be to increase their strength and reduce their exposure. The latter is the reason why we found the mean ratio on the exposed shore to be

  2. Guestimate - investigate how well people estimate the length of lines and the size ...

    so this is the one that is rounded down. Total sample size = 8 + 9 + 13 = 30 YEAR 10 Top Set = 62 X30 = 10.16393643 183 = 10 Middle Set = 83 X30 = 13.60655738 183 = 14 Lower Set = 38 X30 = 6.229508197 183 = 6 My next step is to pick the

  1. Driving test

    By using the intercept (c), I can estimate how many mistakes the average driver makes without any lessons. This means that the average person with no lessons makes 23 mistakes. To pass the test, the number of mistakes would need to be reduced by eight, hence - P = 8x0.2

  2. Throughout this experiment I have decided that I am going to investigate the tensile ...

    The method used for measuring the extension of the wire is a measuring stick and marker on the sample. We can then use the marker on the sample along with the measuring stick to measure how far it moves with each weight added.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work