# Intermediate Maths Driving Test Coursework

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Introduction

GCSE Math’s Intermediate Coursework

Driving Test Coursework

This experiment has the aim of proving the hypotheses (that I shall develop) by handling data and managing it effectively to bring about realistic results. The hypotheses will be based upon test results from a driving school. I am intending to explore the success of males and females in a driving school. I shall do this by testing the number of one hour lessons and the number of errors in a random sample of 80 pupils. I aim to use this data to test several hypothesises.

Data:

The data which I will be using in this investigation has been gathered from an unknown driving school. I am going to investigate in to have a look at the performance of this driving school. The raw data which I have been given is in list form and provides me with the performance of 240 students, of both sexes and includes:

- The number of one hour lessons before successful test.
- The total number of minor errors in test(s) taken.
- The name of the instructor (4 different teachers).
- The day of the test.
- The time of the day of the test.

The data is in no particular order and reflects a large range and variety of results and performances. Here is an example of the data:

Student | Gender of Student | Number of One-Hour Lessons | Number of Minor mistakes | Instructor | Day of Test | Time of Day of Test |

123 | M | 24 | 11 | B | Thur | 9.00 |

211 | F | 18 | 32 | D | Fri | 12.00 |

I have chosen to explore whether males are more successful than females or vice versa. I will break this line of enquiry down into three, manageable hypothesises.

Middle

Number of Lessons

Mean

Range

23.1625

34

With these graphs and diagrams I can see the consistencies and similarities of the sample to that of the original data in the preliminary analysis, and with these results I am fairly confidant that this sample is proportional and un bias. I am now ready to use this sample in my hypothesizes.

Hypothesis 1: The more lessons you take, the fewer mistakes you will make.

This is the assumed thought that with practice you will improve so I will plot my sample’s data onto a scatter graph which will allow me to see if there is a strong negative correlation which I would expect.

From the graph above depicting my sample, you can see there is a very weak negative correlation, almost not visible without a line of best fit. Very few points lay on the line. This is a surprise to me; there must be some reason why this correlation is so weak, this would make you think that there must be some pupils that had the most lessons are the one who aren’t as good at driving and so need to take more lessons and so make a lot of mistakes. Perhaps it is females who are obscuring this fact and males who show a strong negative correlation, this will be my next hypothesizes.

Hypothesis 2: Males perform better in tests than females

Here I will split up the graph I did in the first hypothesizes to show male and female correlations separately which may prove males perform better.

Here the correlation is a little stronger than it was but is still a weak correlation. Only about 4 points lie on the line of best fit.

This has a little or no correlation and is weaker in comparison to the male graph. Only 2 points lie on the line of best fit.

From the line graphs I found that it was a female who made the highest amount of mistakes but also the lowest amount of mistakes. By looking at the graph I also found that a greater number of females were found to have greater mistakes than that of the males. The ale graph has a slightly steeper line than that of the females indicating better performance however both graphs still remain similar so I will use box plots which may let me see a pass rate more clearly for each gender. To make a box plot, I will first need to find the quartiles from my data, to do this I will make a stem and leaf diagram.

Females: No. of lessons

3 | 01122246789 |

2 | 00357788999 |

1 | 0011345556777888999 |

4 | 000 |

3 | 011457 |

2 | 00001223345578999 |

1 | 03344566779 |

0 | 69 |

Median = ½ (n+1)

½(41+1)

21st observation

Lower Q= ¼(n+1)

¼(41+1)

10.5th observation

Upper Q= ¾ (n+1)

¾ (41+1)

31.5th observation

Range= 39 - 10

Females | |

Number of Lessons | |

Q1 | 16.5 |

Q2 | 20 |

Q3 | 30.5 |

Range | 29 |

Minimum | 10 |

Maximum | 39 |

Males | |

Number of Lessons | |

Q1 | 6 |

Q2 | 22 |

Q3 | 29 |

Range | 34 |

Minimum | 6 |

Maximum | 40 |

With these Quartiles I can now plot my box plots.

In the above box plot we can see the males had a bigger spread of results in lessons taken than the females and still had a bigger median. I will now draw a leaf and stem diagram for my next box-plot.

Females: No. of minor mistakes

3 | 11223 |

2 | 0012334889 |

1 | 001223334444556778 |

0 | 23556789 |

3 | 01 |

2 | 012345688 |

1 | 0002344557799 |

0 | 111234456688899 |

Conclusion

The difference in performance between males and females may be affected by the following factors:

- Females may perform better than males because it is widely believed they have a larger concentration span.
- Males may be more confident at the wheel and therefore be less prone to make mistakes.
- Females could have come from a learning deficiency school.
- Males could have come from a rural background and might have had more experience driving using tractors or other machinery.
- Perhaps the Instructor is sexist and is marking males or females more leniently.

Conclusion:

After completing all the graphs I have come to the conclusion that Instructor C was the best Instructor for teaching both males and females due to the instructor’s low mistakes and vast improvement in lessons, the worst instructor I would be instructor D because they were the only instructor to come up with a positive graph. Instructor B was the worst instructor for teaching females. So in summary in my first hypotheses I proved that more lessons means less mistakes and that in my second hypothesis males do perform better than females. However after studying those graphs in which two instructors were worse at teaching the majority of the female sample while males did do better with said instructor A and B, I do believe that the reason females perform worse is because of the instructors A and B.

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

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