# 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

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

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.

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

#### 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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