I will be investigating these factors appropriately with different sampling techniques. I have come to the conclusion that I will not include the results of the tests with missing data. I am doing this because it doesn’t provide me with any information and could have a negative effect on my final results.
Hypothesis
I predict that the pupil with the most lessons will make lees minor mistakes in their tests because the will have had more practice lessons and more time than other pupils, giving them a slight advantage.
Also, by looking at my data I predict that instructor A is the best instructor. The pupils that A instructed on the tests made fewer mistakes, therefore he had the most passes. Although this is only an estimation, I have not taken any other factors into consideration, which I will investigate further on in my analysis of the data I was given.
Investigation
Firstly I will make a scatter graph and plot the number of hour lessons against the number of mistakes made. I took a systematic sample and chose every fifth pupil’s data, as using all of the data would make an unreadable scatter graph. This is a fair sample because it is a good range, and is a fair test. I have chosen these sources of information because they are useful and will give me a good range of results. I will use this data to compare the number of lessons against the number of minor mistakes. I can then investigate these factors and I will see if they are in proportional to each other. I know this data is reliable because it has come from a good source of information, and I am only using the information, which will have a positive affect on my results.
I will perform the following calculations. I will need to find out the percentages of the passes rate. I would do this by finding out the number of passes and fails with each instructor. I would then times the number of passes by 100, then I will divide this number by the amount of pupils who took the test with that certain instructor. This will then give me the percentage of passes with each instructor. This will be very useful because I can see how the pupils with either little or a lot of practice lessons affect the number of passes per instructor. I will check that the calculations make sense by repeating the sum, and making sure that they are reliable and correct. I will show this information in a pie chart.
I will also be finding out how well the pupils performed in the tests with each instructor by using the information and putting it into a box plot. This will enable me to get an overview of the results in general, and it will help me with my evaluation.
By looking at the graph I can see that there is not really a correlation between the number of lessons and the number of minor mistakes made. This leads me to assume that there is something else that will affect this, which is the instructor, so I will plot a graph showing the relationship between the number of mistakes made and the number of lessons taken for each instructor. As each instructor took the tests of different numbers of pupils, I will compare the percentage of passes, rather than the actual number of passes. This way I will make it a fair test.
Because there must be another factor that affects the correlation I will see how the gender affect the number of mistakes made.
By looking at these graphs I have come to the conclusion that there is no correllation, but I can say that there are more male passes than female passes. The male pass rate is 56.8%, whereas the female pass rate is 40.6%.
Box Plot
I drew a box plot in order to show how well the driving tests were performed.
By looking at the graph, you can see that the pupils that Instructor A took, performed the best, because the interquartile ranges are the smallest. Also, it has the smallest range of results. It is skwed though, because the results are bunched up in the positive side of the box plot. This all means that the pupils A insturcted did the best, and all the interquartile ranges are inside the the pass rate of 15 minor mistakes.
Instructor B’s pupils performed quite well in the driving tests, as most of the first interquartile is inside the pass number of 15 minor mistakes.
Insturctor C’s pupils had a big range of results, as the interquartile range is the biggest, at 22 minor mistakes. By looking at the graph, I can see that the number of passes and fails are quite balanced. The second interquartile is 16.5 minor mistakes, just over the number 15, passing the pupil.
Instructor D’s pupils performed very badly, as it is on the negative side of the box plot. This is the opposite to instructor A’s results, as it is skewed at the other end of the box plot. The interquartile range is the second smallest, showing that the pupils performed badly , and had the biggest range of results.
Passes and Fail percentages, in pie charts.
