Comparative stem and leaf diagram of error angles
Key: 0 2=02°
Year 7: 02, 03, 03, 07, 08, 08, 08, 08
Year 11: 02, 07, 08, 08, 08, 08, 08, 08
Year 7
Mode: 8
Median: 7.5°
Lower quartile: 3°
Upper quartile: 8°
Interquartile range: 8-3=5°
Semi-interquartile range: 5÷2=2.5
Year 11
Mode: 8°
Median: 8°
Lower quartile: 7.5°
Upper quartile: 8°
Interquartile range: 8-7.5=0.5°
Semi-interquartile range: 0.5÷2=0.25°
Aware to be on track with my second hypothesis and to avoid endless diagrams, I’ve only chosen year 7 (youngest) and 11(oldest) for this interpretation. Year 11 have a smaller interquartile range. The mode was the same for both but the median was slightly smaller for the year 7. Though 12.5% of both year groups were 2° away from the actual angle but there was 25% of year 7 was 3° away from the actual angle.
75% of year 11 was 8° within whilst 50% of year 7 was at the same category. More of year 11 was further away from the actual angle than year 7.
Conclusion
After interpreting the results, I have reached a conclusion. My hypothesis was that the older a person gets, the better they are at estimating the actual measurement.
There was a slight confusion with all the year groups but I still tried to interpret the results-as clear as I can- to show whether a person does estimate better than others who are younger.
Looking through the interpretations, I found that there is a general concept that year 7 is the year group that is more accurate. Year 7‘s estimates were closer to the actual measurements than the other year groups. The closer the estimate, the more accurate it is.
However, year 10 and 11 had shown that they are better at estimating the angle than the others. This is proven by the graphs, tables, diagrams, etc.
According to the interpretations obtained, the ‘middle’ year groups, year 8 and 9 weren’t as good at estimating since there were big values in their data.
I have proven my point that older people-year 10 and 11-estimate better, with angles, but overall year 7, with smaller values in their data, they are better at estimating.
This hypothesis was more difficult to interpret since I have to be very precise about what I want to interpret. I could improve this by being more specific, like choosing only two year groups-year 7 and year 11- to interpret.
I could have added more people to increase the size of the sample so there is more data to compare.
I could have used a different way of sampling like quota sampling or cluster sampling. Quota sampling is specific; the sample must be of a certain number and a certain category. Cluster sampling is distributing the population into smaller groups. The smaller groups are then selected by random sampling. Though these ways seem ideal, there is a certain degree in them that introduce bias. To avoid bias, I should remain using random sampling and stratified sampling.
Overall Conclusion
The whole point of designing these two hypotheses was to test how well people estimate.
My first hypothesis was that girls are better at estimating than boys. This I proved that girls are better at estimating the length of the line. The boys were better at estimating the angle.
My second hypothesis was that the older a person gets, the better they are at estimating. The year group, year7-the youngest-was better at estimating overall. But I also proved that year 10 and 11-the oldest- was better at estimating with angles.
I had proven that my two hypotheses were right, at a certain degree. This could be clearer if I improved the ways to interpret my hypotheses. My rule for these two hypotheses is that the closer towards the actual measurement, the more accurate they are. And vice versa, the further, the less accurate.
One of the main factors that I could have improved was to increase the size of the sample; 40 was a bit too small and besides the bigger the sample, the more data to compare. Another factor to have considered was the method of how to get my sample. I could have used random sampling with a calculator or a computer; I press the built-in ‘random’ button, which will give me the sample. This surely will decrease the likelihood of introducing bias.
I could have used other ways like pie charts, scatter graphs to interpret the results. More interpretations could clarify which participant(s) is/are more accurate. It would make the conclusion more obvious.
I should have specified the hypotheses; e.g. year 7 are better at estimating the line.