How do I show uncertainty in tables and graphs?

Always include error bars on graphs and a clear uncertainty column or parenthetical values in tables, and state how you calculated those uncertainties such as from the instrument, repeatability, or propagation of errors.

Think of uncertainty like the wiggle room around a measurement; when you measure something you never get a single perfect number, you get a best guess plus or minus some amount. On a graph show that wiggle room with error bars that extend above and below each data point, and in a table give either an absolute uncertainty like plus or minus zero point zero five units or a percentage uncertainty like plus or minus two percent depending on what makes more sense. Say exactly where those plus or minus numbers came from: if they come from the instrument write the instrument resolution or calibration uncertainty, if they come from doing the same measurement many times say the standard deviation or repeatability, and if you combined several uncertain values show the propagation method and write the final propagated uncertainty. Use consistent significant figures so the uncertainty and value match and label axes or table headers with units and the uncertainty format.

A common mistake is showing error bars but not explaining how they were computed, which leaves readers unsure whether the bars mean instrument limits or spread from repeats, so always state the source and method next to the figure or in the caption. Another mistake is using inconsistent significant figures that make uncertainties look more precise than they are, so round the measurement and its uncertainty to the same decimal place. Some people forget to propagate uncertainties when calculated values depend on several measurements, and the quick fix is to use the standard propagation formulas and show the math briefly in a footnote or supplementary table.

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Presenting Uncertainty in Tables and Graphs

1. Show error bars on graphs
2. Give uncertainties in tables
3. Use absolute or percentage format
4. State instrument or calibration source
5. Report repeatability or standard deviation
6. Show propagated uncertainty calculations
7. Match significant figures between values

Common Mistakes in Reporting Uncertainty

1. Not explaining how error bars computed
2. Inconsistent significant figures use
3. Failing to propagate uncertainties

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