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Represent distributions and estimate uncertainty

Quantitative chemistry • Measurements and conservation of mass

Key concepts

What you'll likely be quizzed about

  • Random uncertainty arises from unpredictable variations in repeated measurements, caused by fluctuations in experimental conditions and differences in reading.
  • This uncertainty creates scatter around a central value and affects precision.
  • In contrast, systematic uncertainty is a consistent bias due to factors like faulty calibration or zero error, shifting all results and impacting accuracy.
  • Distinguishing the two helps determine the corrective actions needed: reduce random uncertainty by increasing measurement repetitions and address systematic influence through calibration or methodological adjustments.

Flashcards

Test your knowledge with interactive flashcards

What does overlapping error bars between two means suggest?

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That the difference between the means may not be statistically significant because true values could overlap.

Key notes

Important points to keep in mind

Random uncertainty produces scatter; systematic uncertainty shifts all results.

Use mean for central value; use range, standard deviation, or IQR to describe spread.

For few repeats, estimate random uncertainty as range/2; for many repeats use standard deviation.

Instrument uncertainty commonly equals half the smallest scale division (resolution/2).

Add absolute uncertainties for addition and subtraction.

Add percentage uncertainties for multiplication and division.

Multiply percentage uncertainty by the power when raising to a power.

Report values as mean ± uncertainty with consistent significant figures.

Use error bars to visualize uncertainty and check for overlapping ranges.

Investigate outliers before including them in uncertainty estimates.

Calibration checks reduce systematic uncertainty; repeats reduce random uncertainty.

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