What factors made a person better at estimating the size of an angle or the length of a line Essay Example

What factors made a person better at estimating the size of an angle or the length of a line Essay From this data we made a hypothesis on what factors made a person better at estimating the size of an angle or the length of a line. My hypothesis was that year 10 pupils would be better at estimating both the size of angles and the length of lines than the adults and the year 7 children but adults answers will be closer to the mean on average. To prove this I would have to use the information in the spreadsheet .I first found the mean of angle 1 ,angle2 ,line 1 and line 2 in all of the sample of year ten all of the sample of year seven and all of the sample of the adults because using this I could find the average percentage error of each group because I felt this was essential in trying to prove the hypothesis I made earlier .The means for each were as displayed in the table below:Year 10Year 7AdultsAngle157.7665.4251.25Angle 2142.72141.04147.05Line 13.874.553.6275Line 214.5214.6112.7325At the moment when I produced the data it didnt interpret the data into what I wanted to know bu t I could find using the spreadsheet so first decided to find the percentage error of each group again using the calculation shown in the preliminary testing this was(difference between original and average estimates / actual size/length)* 100But first we thought that in the data there may be rogue results these are called outliers and are values that do not follow the data in a reasonable trend and so can be eliminated using a certain formula that creates upper and lower fences and if values fall outside of these two fences they can be classed as outliers and will be dismissed from the data . To implement this formula we need to find the upper and lower quartiles of the data, so by using Microsoft excel this data was found. The formula to find upper and lower fences to eliminate outliers is as follows:Lower Fence = Lower quartile 1.5 * inter quartile rangeUpper Fence = Upper quartile + 1.5 * inter quartile rangeFrom this we gained our upper and lower fences which wereYear 10Upper FenceLower fenceAngle 173.537.5Angle 2190110Line 15.51.625Line 222.37.7Then we did the same for year 7Year 7Upper FenceLower fenceAngle 192.532.5Angle 220585Line 17.251.25Line 219.57.5And for the adultsAdultsUpper FenceLower fenceAngle 16533Angle 2188.75110.75Line 15.51.625Line 26.87517.675With this data we deleted rogue values which amounted only to three.So now we can find the percentage error without worrying about rogue values influencing what could be a vital difference.Year 10 (%)Year 7 (%)Adults (%)Angle 17.218.96.8Angle 27.99.035.12Line 14.6232Line 216.1716.881.9This gives us an idea of to which group is better at estimating the sizes of angles and the lengths of lines but to see this in another way we can use box plots which are very useful for comparing sets of data from different groups within a certain population. The length of the whiskers can give an indication of how the data is skewed, either positively or negatively. Also the true value can be marked on to compare e ach of the medians to each other. By looking at the box plots , more specifically where the quartiles are marked we can see whether people tended to over estimate or under estimate. If the median is inclined slightly towards the upper quartile then people in that group under estimated more often than not and vice versa.So here are some box plots that compare all the age groups at both angles and lines.From this we see that the adults mean value is closer to the actual value of both angle 1 and angle 2 plus both the values of lines 1 and 2 ,this provides even more evidence to suggest against my hypothesis that years 10 pupils have a better ability at estimating both angles and lines because we have seen this through a percentage error and several box plot diagrams that we gained from using the averages from different groups but to prove my second statement in the prediction that adults estimates would be closer to their mean answer, which effectively means that adults made similar es timates to each other than the year 10 and 7 pupils , I need to use a statistical device called standard deviation this measures the spread of values from the mean, the bigger the value the more the answers are spread from the mean.Angle 1Angle 2Line 1Line 2Year 1011200.952.5Year 715301.53Adults1019.512.4We see the adults standard deviation figure being the smallest for three out of the four categories which proves one of my hypothesis statements correct but the other wrong this is because It was more of a guess than a prediction.Over all the taking all statistical methods used I came to the conclusion that adults were actually better at estimating both angles but it was interesting to see that the adults guesses had a small deviation from the mean (standard deviation) . The year 10 pupils by my calculations were second best ,their percentage errors were either very close to the adults in two out of four cases or dramatically a field from the other angle and line like the other two cases but their was a link between the angle and the line that were quite a bit out from the adult counterparts they were both the larger angles and lines using this information this could of provided another route of investigation to follow but then their was a factor preventing this being time and also looking at the year 7 data they were exactly the opposite to year ten pupils , where as they tended to be further out on the larger values of angle 2 and line 2 ,year 7 tended to be further out on the smaller sets of angle 1 and line 1 so their could have been a connection between this data and their ages or maybe gender but time did not permit us to investigate these fields.If I could reiterate the experiment I would make a more detailed hypothesis inducing me to analyse all possible fields that could of affected a persons ability to estimate the size of angles and lengths of lines an example of this is gender or intelligence but the field that I investigated which was age came out to me with a very clear result , this was that on average the older you are the better you are at estimating the size of an angle and the length of a line ,but we must take into account that we used a random sample of 25% from each group this meant that we could of missed some peoples estimates that could of affected or swayed the results to a different conclusion this could be important. This means the concluding statement may not actually be correct if further investigated with more detail and with more age groups such as year 8 , 9 and 11 but is still correct for the investigation we carried out. What factors made a person better at estimating the size of an angle or the length of a line Essay Example What factors made a person better at estimating the size of an angle or the length of a line Essay From this data we made a hypothesis on what factors made a person better at estimating the size of an angle or the length of a line. My hypothesis was that year 10 pupils would be better at estimating both the size of angles and the length of lines than the adults and the year 7 children but adults answers will be closer to the mean on average. To prove this I would have to use the information in the spreadsheet .I first found the mean of angle 1 ,angle2 ,line 1 and line 2 in all of the sample of year ten all of the sample of year seven and all of the sample of the adults because using this I could find the average percentage error of each group because I felt this was essential in trying to prove the hypothesis I made earlier .The means for each were as displayed in the table below:Year 10Year 7AdultsAngle157.7665.4251.25Angle 2142.72141.04147.05Line 13.874.553.6275Line 214.5214.6112.7325At the moment when I produced the data it didnt interpret the data into what I wanted to know bu t I could find using the spreadsheet so first decided to find the percentage error of each group again using the calculation shown in the preliminary testing this was(difference between original and average estimates / actual size/length)* 100But first we thought that in the data there may be rogue results these are called outliers and are values that do not follow the data in a reasonable trend and so can be eliminated using a certain formula that creates upper and lower fences and if values fall outside of these two fences they can be classed as outliers and will be dismissed from the data . To implement this formula we need to find the upper and lower quartiles of the data, so by using Microsoft excel this data was found. The formula to find upper and lower fences to eliminate outliers is as follows:Lower Fence = Lower quartile 1.5 * inter quartile rangeUpper Fence = Upper quartile + 1.5 * inter quartile rangeFrom this we gained our upper and lower fences which wereYear 10Upper FenceLower fenceAngle 173.537.5Angle 2190110Line 15.51.625Line 222.37.7Then we did the same for year 7Year 7Upper FenceLower fenceAngle 192.532.5Angle 220585Line 17.251.25Line 219.57.5And for the adultsAdultsUpper FenceLower fenceAngle 16533Angle 2188.75110.75Line 15.51.625Line 26.87517.675With this data we deleted rogue values which amounted only to three.So now we can find the percentage error without worrying about rogue values influencing what could be a vital difference.Year 10 (%)Year 7 (%)Adults (%)Angle 17.218.96.8Angle 27.99.035.12Line 14.6232Line 216.1716.881.9This gives us an idea of to which group is better at estimating the sizes of angles and the lengths of lines but to see this in another way we can use box plots which are very useful for comparing sets of data from different groups within a certain population. The length of the whiskers can give an indication of how the data is skewed, either positively or negatively. Also the true value can be marked on to compare e ach of the medians to each other. By looking at the box plots , more specifically where the quartiles are marked we can see whether people tended to over estimate or under estimate. If the median is inclined slightly towards the upper quartile then people in that group under estimated more often than not and vice versa.So here are some box plots that compare all the age groups at both angles and lines.From this we see that the adults mean value is closer to the actual value of both angle 1 and angle 2 plus both the values of lines 1 and 2 ,this provides even more evidence to suggest against my hypothesis that years 10 pupils have a better ability at estimating both angles and lines because we have seen this through a percentage error and several box plot diagrams that we gained from using the averages from different groups but to prove my second statement in the prediction that adults estimates would be closer to their mean answer, which effectively means that adults made similar es timates to each other than the year 10 and 7 pupils , I need to use a statistical device called standard deviation this measures the spread of values from the mean, the bigger the value the more the answers are spread from the mean.Angle 1Angle 2Line 1Line 2Year 1011200.952.5Year 715301.53Adults1019.512.4We see the adults standard deviation figure being the smallest for three out of the four categories which proves one of my hypothesis statements correct but the other wrong this is because It was more of a guess than a prediction.Over all the taking all statistical methods used I came to the conclusion that adults were actually better at estimating both angles but it was interesting to see that the adults guesses had a small deviation from the mean (standard deviation) . The year 10 pupils by my calculations were second best ,their percentage errors were either very close to the adults in two out of four cases or dramatically a field from the other angle and line like the other two cases but their was a link between the angle and the line that were quite a bit out from the adult counterparts they were both the larger angles and lines using this information this could of provided another route of investigation to follow but then their was a factor preventing this being time and also looking at the year 7 data they were exactly the opposite to year ten pupils , where as they tended to be further out on the larger values of angle 2 and line 2 ,year 7 tended to be further out on the smaller sets of angle 1 and line 1 so their could have been a connection between this data and their ages or maybe gender but time did not permit us to investigate these fields.If I could reiterate the experiment I would make a more detailed hypothesis inducing me to analyse all possible fields that could of affected a persons ability to estimate the size of angles and lengths of lines an example of this is gender or intelligence but the field that I investigated which was age came out to me with a very clear result , this was that on average the older you are the better you are at estimating the size of an angle and the length of a line ,but we must take into account that we used a random sample of 25% from each group this meant that we could of missed some peoples estimates that could of affected or swayed the results to a different conclusion this could be important. This means the concluding statement may not actually be correct if further investigated with more detail and with more age groups such as year 8 , 9 and 11 but is still correct for the investigation we carried out.