Maths - statistical driving test

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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


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

Graph 2, the bar chart shows the breakdown of male and female students per instructor, you can clearly see that the statistics of male and female are roughly 50/50 split, again showing that instructor B has had the most number of students.


Investigations

From the previous breakdown I have decided on three areas of investigation.  Each investigation will start with a hypothesis, which I will prove or disprove through the process of in-depth data analysis.

Hypothesis one  :-  The more lessons a student takes the less mistakes they should make.

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.

Hypothesis three  :-  On average males make less mistakes than females.


Hypothesis one

The more lessons a student takes the less mistakes they should make.

Techniques to be used

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

  1. Stratified sampling
  2. Scatter graphs and correlation

Expected outcomes

The first thing I will do is pick a stratified sample I will then plot a scatter graph of lessons against mistakes.  If my hypothesis is correct and more lessons does mean less mistakes then I would expect to see my scatter graph displaying negative correlation.


Hypothesis one  -  Stratified sampling

                A                B                C                D                Total

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Male                29                49                18                20                116

Female        31                51                22                20                124

Total                60                100                40                40                240

A population of 240 students is too many to work with, so in order to investigate my hypothesis I will take a sample of sixty students.  The reason that I chose sixty students is because it is a quarter of the population, however my sample group will be randomly selected.  In order to draw upon accuracy I will use a stratified sample.  To calculate the stratified sample I will divide the previous total population by four, which equals 60, this is now one quarter of the total population.  I will now will ...

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