Determining Uncertainties from Graphs (AQA A Level Physics): Revision Note

Using error bars

• The uncertainty in a measurement can be shown on a graph as an error bar

• This bar is drawn above and below the point (or from side to side) and shows the uncertainty in that measurement

• Error bars are plotted on graphs to show the absolute uncertainty of values plotted

• Usually, error bars will be in the vertical direction, for y-values, but can also be plotted horizontally, for x-values

Determining uncertainties from graphs

• To calculate the uncertainty in a gradient, two lines of best fit should be drawn on the graph:

  • The ‘best’ line of best fit, which passes as close to the points as possible

  • The ‘worst’ line of best fit, either the steepest possible or the shallowest possible line which fits within all the error bars

• The percentage uncertainty in the gradient can be found using:

$\mathrm{percentage}\mathrm{uncertainty}=\frac{\mathrm{best}\mathrm{gradient}-\mathrm{worst}\mathrm{gradient}}{\mathrm{best}\mathrm{gradient}}\times 100\%$

• The percentage uncertainty in the y-intercept can be found using:

$\mathrm{percentage}\mathrm{uncertainty}=\frac{\mathrm{best}\mathrm{y}\mathrm{intercept}-\mathrm{worst}\mathrm{y}\mathrm{intercept}}{\mathrm{best}\mathrm{y}\mathrm{intercept}}\times 100\%$