To try and find a visual connection between the estimations, I will plot a scatter graph of the percentage error of the line against the percentage error of the angle. I will find the average percentage error so that I could compare which was estimated best with one typical value.
Population
My population is 171 pupils, year groups 7-11, in my School who estimated the following:
Line in mm (actual size-
Angle in º
Random Sample
Calculation: Ran# x 171 = nth Person
A random sample of 30 from the population of 171:
*Non – response data so used mean of the whole population.
I will calculate the median as the average because it didn’t take the anomalies in the data into account.
An Unequal Histogram to show the distribution of people estimating a Line.
See Diagram (1)
An Unequal Histogram to show the distribution of people estimating an Angle.
See Diagram (2)
Percentage Error
♦Anomalies
Average Percentage Error
The average line percentage error is 26% …without extreme value is 23%
The average angle percentage error is 38% …without extreme value is 19%
I noticed that the two extreme values as they were affecting the average percentage error hugely and so calculated the percentage error again, excluding them.
Scatter Graph to Find a Relationship between the Estimations.
When plotting these data I noticed 2 extreme estimates and came to the conclusion that the people making these estimates were unfamiliar with the units. Since I am trying to find a relationship between estimations of angles and the estimations of lines, without consideration of units it would be more productive to exclude these anomalies from the data. I then plotted the data again:
Conclusion:
From the information I have collected, I have come to the conclusion that my hypothesis is wrong.
The median for the angle was 45º, which is 7º out of the actual angle and the median for the line was 40mm, which is 9mm out of the actual line. This means that on average people are estimating angles better than lines.
The histograms can be compared to see how concise the estimations were. The line’s range was 95mm whereas the angle’s range was 21º, when not taking the anomaly into account. This clearly shows that pupils are estimating angles within a closer range than lines. Which implies not only that pupils are better at estimating angles but also that pupils give more varied estimations of lines. It is seen in both histograms that people mostly estimated higher rather than lower of the actual size and length.
The scatter graph shows that no one had a percentage error above 50% of the angle whereas they estimate no more than 85% out of the line. This means that generally, within my sample, pupils are better at estimating the size of an angle than the length of a line. The average percentage errors also show this, since the line’s is 23% and the angle’s is 19%. The data is more spread out along the x-axis, which shows that people’s ability to estimate lines is more varied than people’s ability to estimate angles. This evidence shows that more people find it easier to estimate the angle than estimating the line, suggesting my hypothesis is wrong.
Although, a vast number of 17 estimated the angle as 45º, which could suggest that the estimations of the angle were more accurate due to it being only 6º to a familiar angle of 45º. This makes me question how reliable my data is. If I were to investigate this further, I would ask people to estimate two angles.
Evaluation
My conclusions tell me about information collected in the sample; they provide insight into possible correlations in the population I am trying to find out about. When making conclusions about my population I need to consider the reliability of the sample as evidence for the population.
I think my investigation was as fair as I could make possible and some aspects, which I could not control, may have affected it. I only asked girls who were at my school and so is not a fair enough representative to conclude that all pupils would find it easier to estimate angles better than lines and that their estimations would be affected by the appearance.
If I were to rely fully on this investigation to draw specific conclusions on my population I would need more reliable results and so therefore would need to take a bigger sample size, this would also decrease the effect that extreme values have on the sample. Another aspect affecting the reliability of the data to provide evidence for the population is the fact that individuals in the sample didn’t all consider their estimations with the same contemplation (i.e. some people took it more seriously and took more time over it than others). This could be prevented in future samples by perhaps giving short time limits in the estimation periods.
One good aspect of the investigation was the efficiency at which I collected the results, along with the preliminary experiment providing a good basis for the actual one. The range of methods I used to manipulate the data was also a success.
As an extension to my investigation I could extend the tested population to all age groups and gather data as to how well they can estimate the area or volume of an object as well as lines and angles. This would involve the collection of a lot more data.
All in all I think the investigation was very successful as I got conclusive results within my sample, which provided me with a good insight into the estimations of lines and angles. I enjoyed it very much!!!!!!! COOL AND FUN!!!! Hahahaha.
