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  • Level: GCSE
  • Subject: Maths
  • Word count: 5853

Investigation into a driving test.

Extracts from this document...

Introduction

Investigation into a driving test

By Declan Gervin


I downloaded the following database from the Internet.

Number of

Number of

Gender

1 hour lessons

minor mistakes

Instructor

Day

Time

M

8

13

A

Mon

17.00

M

9

9

A

Wed

9.00

M

14

10

A

Fri

13.00

F

15

11

A

Mon

9.00

F

15

15

A

Tue

15.00

F

15

12

A

Mon

14.00

F

20

8

A

Wed

10.00

F

20

14

A

Fri

9.00

F

20

19

A

Mon

13.00

M

20

11

A

Fri

9.00

M

20

12

A

Thur

14.00

M

20

19

A

Fri

9.00

M

20

8

A

Mon

10.00

F

8

10

A

Wed

10.00

F

10

1

A

Thur

9.00

F

10

14

A

Thur

10.00

F

11

3

A

Fri

13.00

F

13

14

A

Wed

13.00

M

15

14

A

Mon

15.00

M

15

9

A

Fri

10.00

M

16

14

A

Wed

17.00

M

17

10

A

Fri

11.00

F

23

5

A

Mon

9.00

F

25

6

A

Mon

15.00

F

27

5

A

Fri

14.00

M

18

16

A

Fri

13.00

M

19

9

A

Thur

10.00

M

19

13

A

Mon

12.00

F

15

11

A

Wed

9.00

F

15

9

A

Mon

16.00

F

19

13

A

Fri

16.00

F

22

14

A

Thur

16.00

M

24

5

A

Mon

17.00

M

25

4

A

Fri

10.00

M

26

3

A

Wed

17.00

M

27

2

A

Tue

17.00

F

16

15

A

Mon

12.00

F

17

16

A

Wed

10.00

M

21

8

A

Thur

16.00

M

22

7

A

Thur

17.00

F

5

27

A

Fri

14.00

F

30

12

A

Fri

10.00

F

11

7

A

Mon

16.00

M

17

8

A

Tue

15.00

F

12

13

A

Thur

17.00

M

8

31

A

Wed

10.00

M

6

23

A

Mon

11.00

F

23

14

A

Wed

14.00

M

9

19

A

Thur

12.00

F

16

17

A

Fri

9.00

M

14

8

A

Fri

17.00

M

19

6

A

Fri

14.00

F

26

9

A

Fri

16.00

F

31

7

A

Tue

12.00

F

14

17

A

Tue

11.00

M

18

19

A

Thur

14.00

M

21

20

A

Fri

17.00

F

11

14

A

Wed

15.00

F

6

27

A

Wed

10.00

M

13

17

A

Fri

16.00

M

24

9

B

Fri

13.00

M

13

28

B

Mon

12.00

M

32

B

Fri

11.00

F

10

22

B

Fri

16.00

F

12

33

B

Thur

14.00

F

17

19

B

Fri

12.00

F

23

3

B

Wed

11.00

F

13

19

B

Fri

10.00

F

26

26

B

Mon

11.00

M

31

1

B

Fri

13.00

M

40

15

B

Thur

12.00

M

19

16

B

Thur

15.00

M

10

30

B

Mon

13.00

F

24

B

Wed

16.00

F

30

15

B

Mon

11.00

F

18

19

B

Fri

10.00

F

17

5

B

Tue

10.00

F

30

24

B

Fri

12.00

M

15

24

B

Wed

13.00

M

34

6

B

Wed

16.00

M

20

15

B

Tue

17.00

M

20

15

B

Mon

16.00

F

39

23

B

Wed

17.00

F

23

10

B

Wed

13.00

F

11

17

B

Tue

10.00

M

16

21

B

Mon

16.00

M

17

19

B

Thur

12.00

M

15

22

B

Tue

12.00

F

34

3

B

Tue

15.00

F

14

17

B

Wed

10.00

F

27

12

B

Thur

15.00

F

36

28

B

Wed

13.00

M

23

12

B

Fri

14.00

M

40

11

B

Fri

9.00

M

31

1

B

Mon

14.00

M

30

3

B

Tue

11.00

F

27

5

B

Wed

11.00

F

27

27

B

Fri

12.00

M

21

15

B

Tue

9.00

M

29

4

B

Thur

17.00

F

31

19

B

Thur

12.00

F

15

10

B

Fri

11.00

F

18

21

B

Thur

17.00

M

40

7

B

Thur

12.00

F

38

13

B

Mon

17.00

M

37

6

...read more.

Middle

F

32

23

D

Fri

14.00

M

40

21

D

Mon

9.00

F

18

30

D

Mon

17.00

M

15

35

D

Wed

14.00

M

29

23

D

Tue

15.00

F

32

17

D

Fri

14.00

M

25

28

D

Thur

9.00

F

17

31

D

Wed

13.00

M

28

26

D

Tue

12.00

M

29

27

D

Thur

12.00

F

31

24

D

Thur

13.00

F

37

18

D

Mon

14.00

F

14

34

D

Tue

13.00

M

40

19

D

Tue

9.00

M

28

24

D

Fri

9.00

F

39

20

D

Thur

9.00

F

10

37

D

Thur

10.00

M

40

20

D

Wed

16.00

By looking through the data there seems to be an awful lot of entries. I will now draw a stem and leaf diagram for the number of minor mistakes against frequency. The stem and leaf diagram is shown overleaf.  

0

4,9,8,8,1,3,9,5,6,5,9,9,5,4,3,2,8,7,7,8,8,6,9,7,9,3,1,5,6,0,3,3,5,7,6,9,5,5,4,6,9,1,9,9,9,5,

1,1,3,8,2,5,4,4,3,6,4,2,5,4,5,9,4

1

2,2,7,9,7,5,5,9,5,6,5,9,1,3,0,1,5,2,4,9,1,2,9,0,4,4,4,4,0,6,3,1,3,4,5,6,2,3,4,9,7,7,9,4,7,9

5,9,0,3,4,6,4,1,9,7,7,6,4,7,5,4,3,0,3,6,9,7,3,3,9,6,7,8,9

2

7,3,0,7,8,2,6,4,4,3,1,2,8,7,4,4,7,6,8,3,1,3,5,6,0,0,1,1,4,2,9,3,6,0,8,6,2,9,2,6,8,1,4,5,7,6

3,1,7,7,7,5,4,8,5,7,3,9,3

3

1,3,6,7,4,2,0,4,2,2,2,3,2,0,2,4,1,1,6,3,2,1,0,0,5,1,4

4

I am now going to test some hypotheses using the stem and leaf diagram.

Hypothesis 1:  Men perform better than females in the driving test.

For this hypothesis I would like to narrow down the number of entries. The steps I will take to do this are as follows.

  • Sort the original database by gender (it’s already been sorted by instructor)
  • Insert a column at the start i.e. before the gender column numbering each group, e.g. instructor A, males, 1-29 etc.

From sorting out this data I can now make out the following table.

Instructor A

Instructor B

Instructor C

Instructor D

Males

29

49

18

20

Females

31

51

22

20

We have already said that the sample is too large to deal with. There are 240 pupils in the sample, so we will now stratify the sample. We will just tale 80 pupils i.e. a third of each of the entries above. Doing it his way we will ensure we have proportional representation. Therefore we have the following numbers.

Instructor A

Instructor B

Instructor C

Instructor D

Males

10

16

6

7

Females

10

17

7

7

...read more.

Conclusion


Hypothesis 4: - Some instructors are better than others.

For this hypothesis I will refer back to the original data sheet and a work out the total number of minor mistakes per lesson for each instructor. From doing this I found that:

Total number of minor mistakes for Instructor A = 57

Total number of minor mistakes for Instructor B = 80

Total number of minor mistakes for Instructor C = 35

Total number of minor mistakes for Instructor D = 42

I will now calculate the average number of minor mistakes for the instructors. I will do this by dividing the total number of minor mistakes by the amount of instructor A, B, C and D. Here is what I found:

Average number of minor mistakes for Instructor A = 0.97

Average number of minor mistakes for Instructor B = 0.81

Average number of minor mistakes for Instructor C = 0.90

Average number of minor mistakes for Instructor D = 1.08

I will now draw bar chart show the average number of minor mistakes against instructor, as shown overleaf. From looking at my results and bar chart I can see that there are less mistakes made when the pupils are with instructor C and there are more mistakes made with instructor B. As there is a great difference in all of the instructors I can safely say that some instructors are better that others therefore proving that my hypothesis is correct.

...read more.

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