OCR AS Physics

Revision Notes

2.2.3 Determining Uncertainties from Graphs

Determining Uncertainties from Graphs

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:

 

Percentage Difference

  • The percentage difference gives an indication of how close the experimental value achieved from an experiment is to the accepted value
    • It is not a percentage uncertainty
  • The percentage difference is defined by the equation:

 

 

  • The experimental value is sometimes referred to as the ‘measured’ value
  • The accepted value is sometimes referred to as the ‘true’ value
    • This may be labelled on a component such as the capacitance of a capacitor or the resistance of a resistor
    • Or, from a databook
  • For example, the acceleration due to gravity g is known to be 9.81 m s-2. This is its accepted value
    • From an experiment, the value of g may be found to be 10.35 m s-2
    • Its percentage difference would therefore be 5.5 %
  • The smaller the percentage difference, the more accurate the results of the experiment

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
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