Graph Uncertainties

01Graph Uncertainties

Error bars

This section covers representing absolute uncertainty on graphs using horizontal and vertical error bars.

Showing uncertainty on a graph

An error bar displays the absolute uncertainty associated with a plotted measurement. Its extent shows the interval allowed by the uncertainty around that point.

A vertical error bar shows uncertainty in the $y$ -coordinate.
A horizontal error bar shows uncertainty in the $x$ -coordinate.
If both coordinates have quoted uncertainties, both orientations may be shown.

For a value $y\pm\Delta y$ , the vertical limits are $y-\Delta y$ and $y+\Delta y$ .

The bars are vertical here because the uncertainties belong to the extension values.

A larger absolute uncertainty produces a longer error bar.

Exam Tip: Centre an error bar on the plotted point and extend it by the quoted absolute uncertainty. Match the direction of the bar to the coordinate whose uncertainty is being shown.

02Graph Uncertainties

Best & worst fit lines

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Choosing the best-fit line

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Finding a limiting fit

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03Graph Uncertainties

Gradient uncertainty

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Compare the fitted gradients

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$\text{percentage uncertainty in gradient} = \frac{|m_{\text{best}}-m_{\text{worst}}|} {m_{\text{best}}} \times100\%$

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$m_{\text{best}} = \frac{26-6}{80-0} = 0.25\ \mathrm{mm\,N^{-1}}$

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$m_{\text{worst}} = \frac{27-4.7}{80-0} \approx0.28\ \mathrm{mm\,N^{-1}}$

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$\frac{|0.28-0.25|}{0.25}\times100\% = 12\%$

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04Graph Uncertainties

Intercept uncertainty

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Compare the y-intercepts

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