Determining Uncertainties from Graphs

• What can be shown on a graph to indicate uncertainty in a measurement?

  Error bars

  
• How are error bars represented on a graph?

  Above and below the point or side to side

  
• What do error bars represent on a graph?

  The absolute uncertainty of values plotted

  
• In which direction are error bars usually plotted?

  Vertical direction for y-values
• What is the purpose of drawing two lines of best fit on a graph?

  To calculate the uncertainty in a gradient

  
• What is the 'best' line of best fit?

  Passes as close to the points as possible
• What is the 'worst' line of best fit?

  Steepest or shallowest line within error bars

  
• How can you find the percentage uncertainty in the gradient?

  Using the formula for percentage uncertainty

  
• How can you find the percentage uncertainty in the y-intercept?

  Using the formula for percentage uncertainty

  
• What are the steps to determine uncertainties from graphs?

  1. Draw sensible scales on the axes and plot data
  2. Draw error bars for each point
  3. Draw the line of best fit
  4. Draw the line of worst fit
  5. Calculate the gradient of each line and percentage uncertainty

  
• What is the formula for calculating the best gradient?

  $\frac{\Delta y}{\Delta x}$
• What are the examiner tips for drawing graphs to gain full marks?

  • Use a sensible scale that occupies paper
  • Label axes with quantity and unit
  • Plot points precisely within 0.5 squares
  • Leave equal points above and below best fit line
  • Draw error bars accurately