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  • Level: GCSE
  • Subject: Maths
  • Word count: 2787

Maths - statistical driving test

Extracts from this document...

Introduction

Maths Coursework

Driving Test

For this piece of coursework I have been given details from a local driving school.  The details fall under four headings, these are gender, number of 1hour lessons, number of minor mistakes and instructor.  My aim is to use this data to further investigate by creating hypothesis, using the data to prove or disprove my theories.  Before deciding on what to investigate I need to look at the breakdown of the collected data, I will then use this information to decide on my investigation topics.

Total data = 240 students.

Instructor                 A                B                C                D        Total

Male                        29                49                18                20        116

Female                31                51                22                20        124

No of students        60                100                40                40        240

Overall in this table there is no gender basis as the male/female split is roughly 50/50.  The instructor with the most students is B with 100 students, and the instructor with the least students is C/D with forty students each.  Also each instructor has roughly 50/50 male and female split in students.

From the breakdown of the data in the table I am able to identify three investigations.  T help me in these investigations I will use a spreadsheet to do all calculations and graphs.


My first graphs show the breakdown of data


image02.png

image03.png

Graph 1

The pie chart clearly shows the breakdown of instructors and students.  B has the most students, followed by A, with C and D having the same amount of students.

Graph 2

...read more.

Middle

19

B

F

23

3

B

F

13

19

B

F

26

26

B

M

31

1

B

M

40

15

B

M

19

16

B

M

10

30

B

F

24

28

B

F

30

15

B

F

18

19

B

F

17

5

B

F

30

24

B

M

15

24

B

M

34

6

B

M

20

15

B

M

20

15

B

F

39

23

B

F

23

10

B

M

16

21

B

F

28

15

C

F

39

1

C

F

23

21

C

M

16

24

C

F

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25

C

M

10

27

C

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32

C

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C

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C

M

32

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D

M

22

9

D

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D

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25

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11

36

D

M

40

4

D

M

29

25

D

M

38

10

D

F

31

24

D

F

24

28

D


Graph 3 - everyone


Graph 4

image04.png

Conclusion for graph 3

Graph 3 shows a scatter graph of lessons against mistakes for the whole population.  If taking more lessons means that you make less mistakes this should be shown on the graph as negative correlation.  On my graph there is no correlation, providing me with no information.

Conclusion for graph 4

Graph 4 is the scatter graph for the stratified sample group of students         and

once again there was no form of correlation, suggesting that my hypothesis may be incorrect because the sample that I picked may not

have been representative of the population, or that they hypothesis itself needs to be refined.  


Hypothesis two

The more lessons a student takes the less mistakes they will make depending on their instructor.  This means that some instructors are better than others.

Techniques to be used

To investigate this hypothesis I will be using two techniques:-

  1. Stratified sampling
  2. Scatter graphs and correlation
  3. Comparison of each individual instructors whole population and stratified sample population.  

Expected outcomes

Hypothesis two is a refinement of hypothesis one; in this next stage of the investigation I have suggested that some instructors are better than others. To investigate this hypothesis I decided to use scatter graphs.

...read more.

Conclusion


Graph 18 & 19 Conclusion

In graph 18 I have plotted the cumulative frequency for both the male and female students.  From my graph I can see that more males make between 5 and 23 mistakes, but more females make between 23 and 40 mistakes.  This again supports my hypothesis that females make more mistakes than males, proving my hypothesis to be correct.  I used my cumulative frequency graph to produce box plots which are displayed on graph 19.  After examining graph 19 I have distinguished that the female students have a bigger range than the males, however the male’s boxplots shows that the males have a bigger inter-quartile range than the females.  Lastly it can be clearly seen on the box plots that the females have a higher median than the males.  These findings once again suggest that the females make more mistakes in comparison to the male students, supporting my hypothesis, indicating that it was correct.  

After distinguishing that my hypothesis was correct I feel that a further investigation could explore the possibility of variables that would have affected the actual validity of my findings.  As my investigation only considered a comparison of mistakes I feel that if I was given the opportunity to repeat this piece of coursework I would take into account the factors which may have contributed towards the students mistakes, these would include the weather, the time of lesson, the day of the lesson, the type of manoeuvre, and many other factors which may have affected the accuracy of my overall outcome.

                

...read more.

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