Estimating the length of the line and the size of the angle

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Aziz Elgindi

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Mathematics Coursework 

          My task is to write a hypothesis and to test how well people estimate and to design and carry out an investigation to test my hypothesis.

        My hypothesis is that people will estimate the length of the line better than the size of the angle because lines are used more commonly than angles are. My hypothesis is also that neither the boys nor the girls will estimate better than one another. I also predict that people in higher sets will estimate the angles and lines better than people in lower sets.

        I will need to carry out an investigation to test my hypothesis. The investigation which I will carry out will be a questionnaire. The questionnaire will be conducted with two lines and two angles which I will ask twenty people in year eleven to estimate the length of the two lines and the size of the two angles. I have chosen twenty people because it will give me a set of eighty results, which is enough to prove my hypothesis. I will do this using a stratified sample to find out how many people I will ask in each set. Once I have found out how many people I will ask in each set, I will randomly pick an even number of boys and girls by picking boys and girls’ names out of a hat. If the number of people that I will ask is an odd number e.g. five, then I will pick two boys from one hat and two girls from the other, then I will mix the names of the boys and girls in one hat and pick out the last one.

To make this a fair investigation, I will draw the angles and lines on plain paper so that people cannot look at the line and count the squares on squared paper. I will also keep the sheet with the lines and the angles separate from the sheet which I will record the results on so that the people I ask cannot look at other people results which could give me inaccurate results because people could copy the ideas of others.

        Once I have collected all of the data, I will put it into tables and draw graphs from the tables to compare the results between boys, girls and between the sets in our year group. I will end up with eighty results, 40 of sizes of angles and 40 of length of lines.  First I will need to work out how many people I will ask in each set of the five sets in year eleven.

        I will first conduct two trial runs of two different ways of recording my results. I will see which is better and why it is better to collect my results. I will only do a sample of 5 people to give me 20 results to test the ways of recording the data. I will randomly pick names out of a hat, one from each of the five sets in year eleven.

        These are the two line and the angles I will use with their sizes written beside them. I did not pick a round number for the sizes because I don’t want it to be a common answer.

Line 1 = 8.7cm

Line 2 = 5.3 cm

Angle 1 = 37°

Angle 2 = 63°

          The first method which I chose was to use a table with certain groups of values in it e.g. 10-19 degrees. Then I would make a tally to record the results. Below are the two tables that I used to collect the data.  

Table used for collecting length of lines          Table used for collecting size of angle

     

As you can see above, I have used two different tables to collect the size of the angles in one table and the length of the lines in the other. I do not think that this table is very efficient because I have to collect make a tally chart in groups, which does not give me accurate results. For the angles the difference between top and bottom value is nine degrees, which is quite a lot. That is why it is not accurate to use this type of table at this present time. I could use groups like this after collecting the information to draw a histogram.

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Another thing which I do not like about this table is that it does not show whom I am asking so that I do not know if I am asking a boy or a girl so I cannot find out the information about the hypothesis on boys and girls. Because I don’t have the names written down I can forget whom I have asked and whom I haven’t so it is confusing.

        This is the second trial for collecting the results. This time I have a table, which contains all of the extra information that I need. I ...

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