# Comparative stem and leaf diagram of error lines

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Introduction

Comparative stem and leaf diagram of error lines

Key: 0 4=0.4 cm

Year 7: 0.4, 0.4, 0.6, 0.6, 0.6, 0.6, 0.9, 1.4

Year 11: 0.4, 0.6, 0.6, 0.6, 0.6, 0.9, 0.9, 1.6

Year7

Mode: 0.6 cm

Median: 0.6 cm

Lower quartile: 0.5 cm

Upper quartile: 0.75 cm

Interquartile range: 0.75-0.5=0.25 cm

Semi-interquartile range: 0.25÷2=0.125 cm

Year 11

Mode: 0.6 cm

Median: 0.6 cm

Lower quartile: 0.6 cm

Upper quartile: 0.9 cm

Interquartile range: 0.9-0.6=0.3 cm

Semi-interquartile range: 0.3÷2=0.15 cm

Aware to 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 7 had smaller values than the year 11. There was 25% of year 7 who were 0.4 cm away from the actual line whilst 12.5% of year 11 was at this category.

The two year groups both had 50% of people who were 0.6 cm away from the actual line. However, 25% of year 11 were 0.9 cm within whilst 12.5% of year 7 were at the same category. 12.5% of year 11 were 1.6 cm within whilst 12.5% of year 7 were 1.4 cm within.

Middle

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

Conclusion

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.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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