Uncertainties and significant figures

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SUMMARY

The discussion centers on the proper way to report results with uncertainties, specifically when a result is expressed to two significant figures (s.f.) and an uncertainty is calculated. A result of 20 with an uncertainty of 0.2 raises questions about the consistency of significant figures in reporting. It is established that the mean can be reported with more significant figures than the original data points, but clarity in the methodology used to derive these numbers is essential to avoid inconsistencies.

PREREQUISITES
  • Understanding of significant figures in scientific reporting
  • Knowledge of uncertainty calculation methods
  • Familiarity with statistical concepts such as mean and standard deviation
  • Ability to interpret and communicate scientific results
NEXT STEPS
  • Research the rules for significant figures in scientific measurements
  • Learn about the propagation of uncertainty in calculations
  • Explore best practices for reporting statistical results
  • Study examples of consistent reporting in scientific literature
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Scientists, researchers, and students in fields requiring precise data reporting, particularly in physics, chemistry, and engineering disciplines.

Benjamin Irwin
If I have a result that can only be quoted to 2s.f., let's say 20, and I calculate an uncertainty of 0.2, then how do I quote this?
 
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Is this the result of taking the mean of data where each data point is only good to 2 significant figures and the standard deviation is 0.2?
If so, I would allow more significant figures for the mean.
If not, you may need to describe how you got these numbers in more detail.
 
Benjamin Irwin said:
If I have a result that can only be quoted to 2s.f., let's say 20, and I calculate an uncertainty of 0.2,

These are inconsistent statements.
 

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