• 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

Representing error bars on a graph

• 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 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
• • This may be labelled on a component such as the capacitance of a capacitor or the resistance of a resistor
  • Or, from a reputable source such as a peer-reviewed data bookletThe accepted value is sometimes referred to as the?'true' value

• 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

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

Step 2:?Draw the errors bars for each point

Step 3:?Draw the line of best fit

Step 4:?Draw the line of worst fit

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