Uncertainties on Graphs

Uncertainties in plotted data are shown on a graph with error bars. An error bar is a line drawn through a plotted point that extends by the absolute uncertainty in each direction, usually with a short cap at each end. If both variables have significant uncertainties, error bars are drawn both vertically and horizontally; if one uncertainty is too small to show on the scale, that bar is left out.Example: A point is plotted at I = 2.0 A, V = 8.2 V, and the uncertainty in V is ±0.3 V. The vertical error bar runs from 7.9 V to 8.5 V, a total length of 0.6 V on the scale.The true value of each point is expected to lie somewhere within its error bar, so a suitable line of best fit should pass through all the error bars (apart from any anomalous point, which should be checked or repeated).Graphs also help you spot errors:
• Random errors make points scatter either side of the line of best fit.
• Systematic errors shift all points the same way. A straight line that should pass through the origin but has a non-zero intercept suggests a systematic error, such as a zero error.If no straight line can pass through all the error bars, either the uncertainties have been underestimated or the relationship is not the one assumed (for example, it is actually a curve).Drawing error bars is the first step in finding the uncertainty in a gradient, which is covered in the next lesson.