Hypothesis One : I predict that Top Sets will have more accurate Angle Results
Percentage Error
This Data will tell me how far the estimates were from the original measurements, and allow me to compare them in a percentage. The number will be a minus if, on average, the predictions were lower than the actual measurements, whilst they will be positive if the estimates were higher than the meaurements.
Year 10 : Angle
Top Set: (115 – 112/ 115) x 100 = 2.6 = 3%
Bottom Set : (115 – 79/ 115) x 100 = 31.3 = 32%
Year 9 : Angle
Top Set: (115 – 108/ 115) x 100 = 6.0 = 6%
Bottom Set: (115 – 81/ 115) X 100 = 29.5 = 30%
Year 8 : Angle
Top Set : (115 – 110/115) x 100 = 4.3 = 4%
Bottom Set: (115 – 123/115) x 100 = - 6.9 = - 7%
Year 7 : Angle
Top Set : (115 – 93/115) x 100 = 19.1 = 19%
Bottom Set : (115 – 109/115) x 100 = 5.2 = 5%
Box Plot Data
The Box Plots allow for a visual comparison of both the spread of data and the overall accuracy of the results.
Top Set Y10 angles: 80,95,100,100,105,105,108,110,110,110,115,115,120,120,135,150
Med: 110 Mode: 120,110 High: 150 Low:80 UQ:120 LQ:113 IQR: 7
Bottom Set Y10 angles : 40,60,70,94,100,110
Med: 82 Mode: 0 High: 110 Low: 40 LQ: 60 UQ: 100 IQR: 40
Top set Y9 angles: 60,100,100,100,100,105,110,110,110,110,115,115,120,120,120,120,123
Med: 110 Mode: 100,110,120 High:123 Low: 60 LQ: 103 UQ: 120 IQR: 17
Bottom set Y9 angles: 25,26,65,65,75,95,100,100,120,120,120,120,130
Med: 100 Mode:120 High: 130 Low: 25 LQ:65 UQ: 120 IQR: 55
Top Set Y8 angles: 60,100,100,100,110,110,110,115,115,120,120,135,135
Med: 110 Mode: 110 High: 135 Low:60 LQ:100 UQ:120 IQR:20
Bottom Set Y8 angles: 94,95,110,120,150,170
Med: 115 Mode: 0 High: 170 Low: 94 LQ: 95 UQ: 150 IQR: 76
Top Set Y7 angles: 65,90,90,90,93,95,97,99,100,100,100
Med: 95 Mode: 90,100 High: 100 Low:65 LQ: 90 UQ: 100 IQR: 10
Bottom Set Y7 angles: 55,60,100,105,105,105,110,110,120,120,120,120,120,120,120,125,145
Med: 120 Mode: 120 High: 145 Low: 55 LQ: 105 UQ: 120 IQR: 15
Evaluation and conclusion
From the evidence I have collected, I can gather that although top sets have more accurate angles, they are barely more so. The averages and spreads of the samples were very close together and the medians were all relatively close to the original predictions. In the case of Y7, however, the bottom set was far closer than the top one. This was the only year where such an anomaly occurred. Perhaps to prevent this in further cases, I would take a different sample and stratify it further. Although this hypothesis has proved to be correct, it was not as decisive as I hoped for and the box plot data surprised me somewhat.
Hypothesis Two: I predict that girls will have more accurate line results than boys
Percentage Error
Y10 : Line
Boys: (12.5 – 16/12.5) x 100 = -28 = 28%
Girls: (12.5 – 14/12.5) x 100 = -12 = -12%
Y9 : Line
Boys: (12.5 – 13.4/12.5) x 100 = -7.2 = -7%
Girls: (12.5 – 14.9/12. 5) x 100 = -19.2 = -19%
Y8 : Line
Boys: (12.5 – 12.7/12.5) x 100 = - 1.6 = -2%
Girls: (12.5 – 12.7/12.5) x 100 = - 1.6 = -2%
Y7 : Line
Boys: (12.5 – 16/12.5) x 100 = -28 = -28%
Girls: (12.5 – 10.8/ 12.5) x 100 = 13.6 = 14%
Box Plot Data
Y10 Boys Line: 10,11,13,13,14,15,16,17,18,20,20,25
Med: 14.5 Mode: 13,20, High: 25 Low: 10 LQ: 13 UQ:20 IQR : 17
Y10 Girls Line : 9,10,11,11,12,12.5,13,13,15,18,30
Med: 12.5 Mode:11,13 High: 30 Low: 9 LQ:11 UQ:15 IQR: 15
Y9 Boys Line: 11,11,12,13,13,14,15,15,15,15,15,15,17,22
Med:15 Mode: 15 High: 22 Low:11 LQ: 13 UQ:15 IQR: 2
Y9 Girls Line: 10,12,12,12.5,13,14,14,15,15,15,16,16,30
Med: 14 Mode: 15 High: 30 Low: 10 LQ:12 UQ: 15.5 IQR: 3.5
Y8 Boys Line:8,9,11,12,13,15,15,15,21,21
Med: 14 Mode: 15 High: 21 Low: 8 LQ:11 UQ: 15 IQR: 4
Y8 Girls Line: 10,10,11,12,13,13,15,15,16
Med: 13 Mode: 10,13,15 High: 16 Low: 10 LQ:10.5 UQ: 15 IQR: 5
Y7 Boys Line: 7,10,11,11,13.2,15,15,15,15,15,15.8,20,25,26,26.5
Med: 15 Mode:15 High: 26.5 Low: 7 LQ:12 UQ: 17.9 IQR: 15.9
Y7 Girls Line: 4,6,7,7,8,9,9,9.5,10,13,17,20,22
Med: 9 Mode: 9 High:22 Low:4 LQ:7 UQ: 15 IQR: 7
Evaluation and Conclusion
The results that I have found whilst assessing this conclusion prove that Girls are just as accurate at guessing line lengths as boys. The Box plots support this theory; although the group with the most accurate median was a female one (Y10) these results are not constant with the rest of my findings. The spread of data was quite large with most of the groups, but yet again, one group stands out as having a quite concise sample : the Y8 girls, although their median is quite a distance from the actual measurement. These estimates are, on average, quite accurate. These findings do to support my hypothesis to an extent, but not to such a level that I would assume that gender has any fundamental influence on the accuracy of angle estimates.
Hypothesis Three: I predict that older pupils will have more accurate results
Y10
Angle (115 – 96/115) x 100 = 16.5 = 17 %
Line: (12.5 – 15/ 12.5) x 100 = -20 = -20%
Y9
Angle: (115 – 92/115) x 100 = 20 = 20%
Line: (12.5 – 13.6/12.5) x 100 = -8.8 = -9%
Y8
Angle: (115 – 108/115) x 100 = 6 = 6%
Line: (12.5 – 12.8/12.5) x 100 = -2.4 = -2%
Y7
Angle: (115 – 103/115) x 100 = 10.4 = 10%
Line: (12.5 – 13.6/12.5) x 100 = -8.8 = -9%
Box Plot Data
Y10 Angle: 40,60,70,80,94,95,100,100,100,105,105,108,110,110,110,110,115,115,120,120,120,135,150
Med: 105 Mode:110 High:150 Low:40 LQ:95 UQ:115 IQR: 20
Y9 Angle: 25,26,60,65,65,75,95,100,100,100,100,100,100,105,105,110,110,110,110,115,120,120,120,120,120,120,120,120,123,130
Med: 110 Mode:120 High:130 Low:25 LQ:97 UQ:120 IQR:23
Y8 Angle: 60,94,95,100,100,100,110,110,110,110,115,115,120,120,120,135,135,150,170
Med:110 Mode:110 High:170 Low:60 LQ:100 UQ:120 IQR: 20
Y7 Angle: 55,60,65,90,90,90,93,95,97,99,100,100,100,105,105,105,110,110,110,120,120,120,120,120,120,120,125,145
Med:105 Mode: 120 High: 145 Low: 55 LQ:92 UQ:120 IQR:28
Y10 Line: 9,10,10,11,11,11,12,12.5,13,13,13,13,14,15,15,16,17,18,20,20,25,30
Med:13 Mode:13 High:30 Low:9 LQ:11 UQ:17.5 IQR: 6.5
Y9 Line:
10,11,11,12,12,12,12,12.5,13,13,13,13.2,14,14,14,15,15,15,15,15,15,15,15,15,15,16,16,17,22,30
Med:14 Mode:15 High:30 Low:10 LQ:12 UQ:15 IQR:3
Y8 Line:
8,9,10,10,11,11,12,12,13,13,13,15,15,15,15,15,16,21,21
Med:13 Mode:15, High: 21 Low: 8 LQ:10.5 UQ:15 IQR:4.5
Y7 Line:
4,6,7,7,7,8,9,9,9.5,10,10,11,11,13,13.2,15,15,15,15,15,15.8,17,20,20,22,25,26,26.5
Med: 12 Mode:15 High:26.5 Low: 4 LQ:9 UQ:16.4 IQR: 5.4
Conclusion and Evaluation
Judging by the results I have found, I can conclusively say that my hypothesis was wrong. I can find no evidence to suggest that older pupils have a higher degree of accuracy when making their predictions. Indeed, I have discovered that all the year groups are equally able to undertake this task and have done so, all within a reasonable degree of accuracy. I have also noted that overall, the line estimates were on average closer to the actual measurements, but had a wider spread of data, whereas the angle medians were further off but the data itself more concise. Perhaps this is to do with the fact that most people can recognise certain angles visually eg. 90 , 180 , 45 ,270 etc. and so would naturally connect the angle with the nearest recognisable one. This would explain the concise data. The variation in means could be explained by the difficulty in distinguishing between one angle and the next. An angle is a very small measurement and therefore any exact results were unlikely. With lines, however, there are no reference points to use as templates. This would account for the much larger data spread that this sample gives. In conclusion, the age of a person does not appear to be an influence when estimating accurately, and all year groups managed to keep a quite good level of accuracy.
