French Holidays
4 star(s)
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 |
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 |
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.
This student written piece of work is one of many that can be found in our GCSE Beyond Pythagoras section.
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