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• Level: GCSE
• Subject: Maths
• Word count: 3798

# I have decided to test a group of pupils in order to investigate if there is a difference in ability to estimate the size of an angle and the length of a line.

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Introduction

I have decided to test a group of pupils in order to investigate if there is a difference in ability to estimate the size of an angle and the length of a line. The factors that can be looked at are as follows: -

• Set
• Gender
• Location of line / angle

In order to test all these factors I will need a range of pupils selected at random from a range of sets. I have decided that 18 pupils, selected from three sets will be appropriate for my investigation. I will select 6 pupils, three male and three female, from sets 1, 3 and 5. The quota of eighteen pupils I will use from the sets will give me an appropriate, representative sample.

Since there are three different ability sets of pupils (sets 1, 3, and 5) that are to be tested, with a wide gap between them I should be able to see clearly from any graphs and tables I draw any results trends or patterns which may suggest that the intelligence of a pupil does affect there ability to estimate the length of a line and the size of an angle.

I have selected an even number of male and female subjects for my investigation with the same number from each ability set of pupils, using this information and results I collect I should be able to draw conclusions upon whether the sex of a pupil determines there ability to estimate the length of a line and the size of an angle.

I aim to also see if the location of the line or angle determines a person’s ability to estimate the length of a line or size of the angle. I propose to do this by placing various lines and angles within shapes, i.e.

Middle

From initially looking at my results I can see that I have calculated lots of statistical data around which to bas e my conclusions. Looking at line 1 people seemed to find it reasonably easy to guess its length since the mean is within a few centimetres of its actual value and the interquartile range, i.e. the spread of the middle half of the data is small, the median and modal values also suggest that this line was easy to estimate in length. From looking at the cumulative frequency graph for line 1 you can clearly see that there isn’t much difference between the median and the actual length suggesting that this line was the easiest to estimate. From looking at line 1 people didn’t find it difficult to estimate already it appears that the location of the line may affect the ability to estimate. Looking at the histogram of line 1 it also shows that modal value was again close to the actual length (mode being the number of items which occurs most frequently in a frequency table.) showing that people were frequently guessing close to the actual length. The low standard deviation (Standard deviation meaning a more detailed way in which the data is dispersed about the mean as the centre of distribution.) indicates that there is a much tighter distribution of results where most of the values are within a narrow range either side of the mean, which is true in this case.

Looking at line 2 people seemed to find it quite hard to estimate, as the mean value is 31.57 cm and the actual length 17.5 cm, which there is a difference of 14.07 cm. This shows people where actually mislead by the shape which was a randomly curved shape.

Conclusion

The results are reliable and proved that my part of my predictions were correct and proved that some were incorrect and the results were surprising to see and this proves that the experiment was carried out correctly. The results were reliable, but a few errors did occur i.e. anomalous results. This could be due to human error people being mislead by the size of the shape etc. I collected too much data and there was not enough time to analyse and evaluate it. I didn’t have time to draw conclusions from results in different ways covering many of the variables, which were stated in my plan. I concentrated on a few in detail rather than having lots of unclear results.

These problems could be over come using more precise equipment to measure the lines for testing making the results more reliable. If I had more time I would be able to cover the whole investigation in much more detail and look at the variables, which were stated in my plan.

The conclusions, which were made, are true for the lines that I used in my investigation and the males and females, which were tested, in my investigation but I can’t say that these are true for all lines and all males and females. Further investigations would have to be carried out to prove my conclusions.

If I were to do the experiment again I would use a stratified sample, as this would be easier as a quota sample took a long time to put together. I would try discovering whether ability sets affect a person’s capability estimate. I would also ask a larger number of male and females to see if gender does affect the ability to estimate.

This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.

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