Determining Uncertainties from Graphs (DP IB Physics): Revision Note

Determining uncertainties from graphs

Uncertainty bars

• The uncertainty in a measurement can be represented on a graph as an uncertainty bar, or 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

Representing uncertainty bars on a graph

Calculating uncertainty in gradients and intercepts

• 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 line of best fit passes as close as possible to all the points. The steepest and shallowest lines are known as the worst fit

• The percentage uncertainty in the gradient can be found using the magnitude of the 'best' and 'worst' gradients:

percentage uncertainty = 

• Either the steepest or shallowest line of best fit may have the 'worst' gradient on a case-by-case basis

  • The 'worst' gradient will be the one with the greatest difference in magnitude from the 'best' line of best fit.

  • The equation above is for the case where the 'worst' gradient is the shallowest.

  • If the 'worst' gradient is the steepest, then the 'worst' gradient should be subtracted from the 'best' gradient and then divided by the best gradient and multiplied by 100

• Alternatively, the average of the two maximum and minimum lines can be used to calculate the absolute uncertainty:

absolute uncertainty =

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

percentage uncertainty = 

absolute uncertainty =