AQA A Level Physics

Revision Notes

1.2.3 Determining Uncertainties from Graphs

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

Error Bars, downloadable AS & A Level Physics revision notes

Representing error bars on a graph

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

Worst and Best Lines of Fit

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

Worked Example

On the axes provided, plot the graph for the following data and draw error bars and lines of best and worst fit.

Worked Example: Using Error Bars, downloadable AS & A Level Physics revision notes

Find the percentage uncertainty in the gradient from your graph.

Step 1: Draw sensible scales on the axes and plot the data

Points Plotted, downloadable AS & A Level Physics revision notes

Step 2: Draw the errors bars for each point

Error Bars Drawn, downloadable AS & A Level Physics revision notes

Step 3: Draw the line of best fit

Line Of Best Fit, downloadable AS & A Level Physics revision notes

Step 4: Draw the line of worst fit

Line Of Worst Fit, downloadable AS & A Level Physics revision notes

Step 5: Work out the gradient of each line and calculate the percentage uncertainty

Best & Worst Gradients, downloadable AS & A Level Physics revision notes

Exam Tip

When drawing graphs make sure to follow these rules to gain full marks:

  • Ensure the scale is sensible and takes up as much paper as possible
  • Label the axes with a quantity and a unit
  • Precisely plot the points to within 0.5 squares
  • Leave a roughly equal number of points above and below the best fit line
  • Draw the error bars accurately

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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