We are conducting an investigation to discover how accurate people in our school are at estimating the lengths of lines and the sizes of angles.

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Samantha Brown 11C

 

Statistics Coursework

We are conducting an investigation to discover how accurate people in our school are at estimating the lengths of lines and the sizes of angles. My hypothesis will be based on sizes of lines and angles because if we tested people by using measurements like area and volume we may instead end up testing their ability at calculating these things instead. Some people find calculating these values harder than others.

Hypothesis

  • It is easier to estimate the size of acute angles than obtuse.

I think that it is easier to estimate the size of acute angles than obtuse angles because they are easier to visualise than larger angles. For example, the angles 90˚ and 45˚ are easier to visualise than angles like 165˚ and 130˚.

  • Year 11 students can estimate the length of the straight lines more accurately than Year 7 students.

I have made this hypothesis because I think that Year 11 students have had more experience at using and estimating lengths due to the fact that they are 4 years older than year 7 students.

Method

I will be using a total of 60 students from which to collect the data needed for this investigation, 50% from Year 11 and 50% from Year 7. (However only 30 people from year 11 will be used for the investigation into my 1st hypothesis). This way I can compare the results I get from each year and either prove or disprove my hypotheses. I am using students from Years 7 and 11 because I believe this will make the difference between my results very different and will also show how we progress from Year 7 through to Year 11.

Two angles will be drawn onto a blank piece of A4 paper-one measuring 52˚ the other 156˚. These will be used to test candidates for my first hypothesis. A straight line measuring 13.7cm will be drawn on another piece of plain paper. This will be used to test candidates in my second hypothesis. We have chosen these measurements as they are not easily recognised, and so we will definitely be testing the candidates estimating, not recognising, skills.

Candidates will be taken to an empty room where they will be shown the angles or line; depending on which investigation they have been chosen to participate in. The candidates will then be asked to each write down what they believe the size of the line/angle to be. After collecting all of our results we will put them in graphs to analyse and compare them.


Sampling

To make sure that a representative sample of students is used, I will take a stratified random sample for the data collection. As we are using students from both Years 7 and 11 we will use class lists to establish how many boys and girls were in both years, and also the appropriate totals of students. There are a total of 236 students and for the purposes of our investigation a stratified random sample of 60 must be taken.

The stratified random sample that I took provided me with the number of students I should use from each year and also how many of each sex.

I used a stratified random sample because if a simple random sample had been taken everybody would have an equal chance of being selected, and so in theory this could result in a biased result e.g. 60 year 11 boys.

In a stratified random sample the original group is divided into smaller categories called strata. A random sample is then taken from each stratum in proportion to its size. My stratified random sample tells me how many students are needed for each sex and year group;

After finding how many students are needed I must decide which students to use from years 7 and 11. To do this I took all of the class lists from each year and numbered the girls and boys separately: In year 7 the girls were numbered from 1-50 and the boys 1-69. In year 11 the girls were numbered from 1-51 and the boys 1-66. Then, to randomly pick which people from the two years I would use in the investigation I used the random function on my calculator.

To do this I enter into my calculator the total number from which the samples are to be taken, (e.g. Year 7 girls=50), press 2nd function followed by random and then press equals. I press equals until I have the number of candidates I require (e.g. Year 7 girls=13). However, the random function does not always give whole numbers-in many cases it provides numbers with 1 or more decimal places. Because of this I am careful to round up all numbers and check that I am not repeating numbers whilst sampling the group.

Join now!

I have included a class list on the next page to demonstrate how the males and females were numbered separately.


Pilot Survey

Before carrying out the main investigations I conducted a pilot survey to test if my proposed method would work efficiently. This is done to discover any problems in the method used on a smaller scale-instead of testing a large number of people we instead tested only 5 boys and 5 girls from my maths group.

Pilot Survey Analysis

Our pilot has revealed that there are some problems with the way we had originally ...

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