In the second section the ability to estimate the size of five angles in five different situations. Each of the angles were measured accurately before in degrees and then the pupils were asked to estimate.
People that were being tested were given no time limit to estimate the size of the lines and angles.
So I am able to collect results from all sets. I will test one of the three sets, and two other people will test another set each. The tests that each pupil will undertake will be identical no matter there sex, or set.
After data collection is complete and the results have been recorded in tables I can then begin to analyse the data in order to see if there are any trends or patterns. To make analysis of the data easier I will draw various graphs from the results. From the results data I will: -
- Draw histograms to determine the mode for the sexes, the set that the pupils are in and for each line
- Draw cumulative frequency curves to determine the median and interquartile range for the data
- Draw frequency tables and determine the mean and standard deviation from these
To ensure that I check the trends and patterns for each of the three aspects mention above I will have to group the data in different ways for each aspect I test. This means that in order to draw up graphs for the set of the pupils I will draw three cumulative frequency graphs, one for each set of pupils and for each line so in total I will have to draw 15 cumulative frequency and histogram graphs.
To draw the results for the sex category I would have to draw 10 graphs, one for each line of each sex.
In order to draw the results for the line category I would simply need five cumulative frequency graphs one for each line where the data for all the sets and sex of the people is used.
Conclusion
Looking at results table 8.1, which compiles all of my results for the investigation to see if the location / shape of the line affects the ability to estimate the length of the line. In order to make comparison of the results on the graph easier I have added a line to the cumulative frequency graph, which shows the actual length of the line, which is useful as, it shows whether the median (the median is where data is arranged from smallest to largest and the middle number is selected.) is close to the actual length.
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. From looking at the cumulative frequency graph for line 2 it clearly shows this, as there was also a greater interquartile range, which means there was greater measure of spread so people where unsure of their estimates. From the shape of the cumulative frequency graph the line shows a more widely spread set of data. Looking at the standard deviation of line 2 this shows a high dispersion (i.e. a large spread of data away from the mean). So estimates will cover a very wide range of lengths.
Comparing these results to the results for line 1 it is clear to see that people found it much more difficult to guess its length. Line 2 was the randomly curved line which obviously deceived the test subjects into thinking it was longer than it actually was since the actual size of the line was 17.5 centimetres yet from the results I have collected the mean was calculated to be 31.57 but with a high interquartile range it shows people weren’t all consistent in there guesses as with line 1. Comparing both cumulative frequency graphs they both clearly show that for line 1 the distribution of data was bunched around the middle half and for line 2 the data was spread proving what I have stated, people found line 1 the easiest to estimate than line 2.
Looking at line 3 people seemed to find it reasonably easy to guess its length since the mean is within a few centimetres of the actual length. This line was part of a triangle, which I thought people would find it harder to guess but from my results you can clearly see that this is not entirely true, people found this easier to estimate. Looking at the interquartile range, which is again a small value, and the median and the modal values also suggest that most people found this line easier to estimate its actual length. The small interquartile range shows a much tighter distribution around the median and looking at the shape of the cumulative frequency graph this proves that this is true. Looking at the low standard deviation there was a much tighter dispersion of results.
Looking at line 4 people found this line very easy to estimate. The mean value was very close to the actual length and there was only a difference of 0.47 cm between them. I found people could easily estimate the length of this line. The modal value from the histogram was quite close to the actual length but the median was the same value as the actual length, but there is a high dispersion of results, which shows that the guesses weren’t consistent but accurate. The higher standard deviation indicates the high dispersion and also from looking at the shape of the cumulative frequency graph. From analysing the graph this indicates the high interquartile range, which show a much greater measure of spread, but guesses were precise.
Comparing these results to the results of line 4 people found it much easier to guess the length of line 4 than line 3 as the mean value was 20.67 cm and the actual length was 20.2 cm. Line 4 was the circle and people found this the easiest to guess out of the five lines. Line 4 had a much higher interquartile range, which suggests that there was a greater measure of spread of results, which meant that there were a wide variety of guesses. Line 3 had consistent results with a tighter dispersion so there were accurate guesses whereas line 4 there was a large measure of spread but precise estimates. This proves people had the ability to estimate accurately but some people were unsure so the data was spread greater. Line 4 was the circle and people found this much easier to guess than the straight line in the triangle, which is surprising to find.
From analysing the results of line 5 people also found this line easier to estimate, as the mean was also quite close to the actual length. The mean was 26.67 cm and the actual length was 28 cm with only a difference of 1.33 cm, which suggests people, again had the ability to estimate consistently. The interquartile range was higher but it shows a distribution not as tight and dispersion not as high. The modal value from the histogram and median were also very close to the actual length with the median only 0.5 cm over the original length. The standard deviation was higher but indicates a higher dispersion of results but some of the results were bunched around the middle half.
From analysing all of the lines together it is clear to see that people found it the easiest to guess the length of the circle. It is surprising to find this as I thought the circle would be the hardest to estimate due to the fact there are no straight lines. Also people where able to guess the length of the lines even if they were part of a shape, which in my prediction I said this would be difficult for people to estimate. People may have found this easier as there were other lines so it was easy to estimate or people were just having wild guesses. People also found it easier to guess curved lines than straight lines, which again is surprising. People found it harder to estimate the length of line 2, which was the randomly curved line and people where having guesses, which exceeded the actual length. Looking at results table 8.1 most of the means where very close to the actual length of the lines but most of the lines had a wider spread of data.
From my original predictions I believed that people would find it harder to estimate the length of lines depending on their location/ shape. I was surprised to find this wasn’t true for most of the lines and I believe it was due to the fact that there was other lines with the shape and people used the length of those to work out the length of that particular line. People found it easier to guess the length of circle because of the shape no lines people were using their ability to estimate and people also were just have wild guesses. I thought the circle would be harder due to the fact of its shape and I thought would just have a wild guess and not try and use their ability to estimate. The mean was quite close being 20.67 cm and the actual length being 20.2 cm, which is incredibly close. I thought people would find it easier to estimate the length of the straight line rather than the circle but as you can see from my results this is not true.
I thought people would find line 5 hard to estimate which was the zigzag line but people again were having guesses quite close to its actual length. I think this one was easier because of the straight lines all people had to do was estimate each straight line and then add each estimate together. The mean on this line was quite close with 26.28 cm and the actual length being 28 cm.
I thought people would fid it hard to estimate the length of the randomly shaped line and this was true. People were obviously mislead by its shape and there was a wide range of results.
I found that the lines, which had a high interquartile range, were the lines people seemed to have the most difficult estimating apart from line 4, which was found to be the easiest line to guess. The lines that had the small interquartile range were the lines that people found easier to estimate as most people tested were having the same estimates. The line that had the highest standard deviation was the line that people found the most difficult to estimate.
Looking at results table 8.2, which compiles all of my results from this investigation to see if gender affects the ability to estimate the length of a line. In order to make some conclusions and some comparisons I have added an extra line to the cumulative frequency graph, which shows the actual length of the line.
From looking at line 4 I have drawn various graphs to see gender does affect the ability to estimate. Looking at the results from the females it is also clear to see that the mean was quite close to the actual length with the mean being 23.70 cm and the actual length being 20.2 cm. The median and modal values suggest that the females found it easy to estimate the length of the line. Females have a much tighter distribution due to the small interquartile range. This shows as the females had a much lower standard deviation. Looking at the shape of the cumulative frequency graph show that the females did have a very tight distribution around the median. The females estimates were much more consistent.
Looking at the results of the males they had a higher dispersion of data because of the high interquartile range. This shows with the males having a high standard deviation. There was a greater spread of results away from the mean. Looking at the shape of the cumulative frequency graph the line shows a more widely spread set of data and therefore a larger interquartile range.
Comparing the results together the female data was bunched around the middle half of the graph, this means the estimates for them were around the same, whereas the males had a much larger spread of data which means the estimates for them weren’t the same. The female estimates were more consistent than the males and the males had a much higher interquartile range because of the widely spread data. The males mean was much more closer to the actual length than the females, with the males having a mean of 19.35 cm and the actual length being 20.2 cm which is a difference of 0.85 cm. The females had a mean of 23.70 cm with the actual length being 20.2 cm, which is a difference of 0.35 cm so the males were having much more accurate guesses than the males.
From my original prediction I said that the gender would not affect the ability to estimate. There is however a difference between the two but it is a large difference. I think the difference is because we asked the wrong girls. If we had used a different sample instead of a random sample then I may have been able to select people and then the results may be different then. It was due to the people I asked. The females may have been having wild guesses and the males may have had educated guesses but it was all due to the people that were tested. Although the males were having more accurate guesses the females were more consistent in their estimates so the females were able to estimate it was just because of the comparison between the two that there is a difference.
Evaluation
From the experiment I investigation I obtained good results and I found the experiment most enjoyable. The experiment was carried out to what I had planned and this show from my investigation. I obtained many sets of results showing people’s ability to estimate the length of a line and how it is affected by the shape or location of the line. My results were accurate but from analysing them it is clear to see that I obtained a few anomalous results. The results were accurate to 1 millimetre shown by the meter ruler.
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.