1.2.3 Determining Uncertainties from Graphs

• 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

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

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