# GCSE Statistics Coursework

Kevin Sharp

Statistics GCSE coursework

Kevin Sharp

In my DT lesson our teacher told us to draw a 25cm line and I drew mine too big and the teacher told me to get better at maths. I did not think this would improve my ability to estimate a length of a line so decided to find out. The questions I thought up are:

1) Is there any relationship between estimating a length of a straight line linked to mathematical ability?

Null hypothesis: There is a relationship between them.

Alternative hypothesis: There is no relationship between them.

2) Does the estimation of a non straight line improve after practice?

Null hypothesis: Practice improves the estimation of a non straight line.

Alternative hypothesis: Practice doesn’t improve the estimation of a non straight line.

3) Does a 14/15 year olds ability to estimate the length of a straight line fit a normal distribution?

Null hypothesis: A 14/15 year olds ability to estimate a straight line fits normal distribution.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line doesn’t fit normal distribution.

4) Are a 14/15 year olds ability to estimate a straight line more accurate than estimating a non straight line?

Null hypothesis: A 14/15 year olds ability to estimate a straight line is more accurate than estimating a non straight line.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line is less accurate than estimating a non straight line.

To get this data I am going to test 14/15 year olds in England as they have the same amount of education and experience. 14/15 year old can be used as a sample of England’s population to some degree of accuracy. They also have worked a lot with rulers so they know the approximate length of 30cm and 15cm lines. Year 10 at Stamford school and Stamford High School represent a small sample of year 10 pupils in England. Year 10 in the Stamford Endowed schools is an accurate choice as every person has have the same education and experience and the data is very easy to collect. Every person has used the same facilities, books and material and the teachers have all been taught the same. Although there maybe some problems and anomalies with this sample because someone maybe away, someone maybe blind or have eye problems and someone might be handicapped. For each question I will use a certain sample of year 10’s at Stamford Endowed schools.

To get this data I need to get a person to estimate a line and a non straight line in an experiment. I need to make the experiment fair, so I need the same controlled experiment for each person who does the experiment. The pupils will enter a room and look at a straight line and a non straight line and ask them to estimate it in mm. There are many things which need to be kept the same and precautions to take so the data I get is accurate.  To make the experiment fair I need to:

Make the time given for each person to look at the line the same.

Make each person the same distance, angle and height away from the line.

Keep the line the same length, same thickness, same colour, on the same background and don’t make the line too big or small.

Make sure the person is on his own and there is no distractions and leaves without conferring with anyone or telling anyone anything.

Give each person the same instructions and tell them what unit and what degree of accuracy to estimate in.

Keep the same lighting conditions with each person.

Make sure there are no objects to compare the line with.

Tell the pupils something to inspire them to do the experiment to their best ability like there is a prize for the most accurate answer.

Make sure no one has eye problems so they don’t have to do it and cause anomalies.

The lines they have to estimate look like this:

Actual lines which were estimated are at the back of the project.

I got this trial data by doing this experiment and got these results:

The red results are for the three practices and are not needed.

The problem is that 14 of the 26 results in the first column are been estimated in cm so to improve the experiment I made sure the pupils were told clearly to estimate in mm.

I then got this data:

Some are still estimating in cm but not as many as in the trail data.

Question 1) Is there any link between estimating a straight length of a line and mathematical ability?

Null hypothesis: There is a relationship ...