AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Represent uncertainty in a data point on a graph using error bars.
Full specification wording
Limitation of physical measurements: Represent uncertainty in a data point on a graph using error bars.
Error bars show the uncertainty attached to each plotted value.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 5 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Error bars show the uncertainty attached to each plotted value. For a point (x, y), the absolute uncertainty in the dependent variable gives a vertical bar from y − Δy to y + Δy; uncertainty in the independent variable gives a horizontal bar from x − Δx to x + Δx. Draw bars with a ruler, centred on the plotted point, with caps if you wish. For example, a current of 0.50 A with uncertainty ±0.02 A is plotted as a vertical bar from 0.48 A to 0.52 A. If only one variable has a stated uncertainty, draw only that bar. Error bars let you judge whether a line of best fit is consistent with the data and whether a point is anomalous.
What earns the marks
- Identify which variable carries the stated uncertainty and whether it is the independent or dependent variable.
- Calculate the upper and lower limits by adding and subtracting the absolute uncertainty from the plotted value.
- Draw the bar centred on the point, of correct total length 2Δy or 2Δx, using a sharp pencil and ruler.
- Add caps or clear end markers so the extent of the uncertainty is unambiguous.
- If both variables have uncertainties, draw both vertical and horizontal bars to form a cross.
- Keep the scale consistent so the bar length genuinely represents the uncertainty.
Common mistakes and how to put them right
Drawing the bar from the point to one limit only, so the length represents Δy rather than 2Δy.
Put it right by centring the bar on the point.
Using the percentage uncertainty as if it were an absolute uncertainty.
Put it right by converting to an absolute value before plotting.
Drawing bars on every point when only one variable has a stated uncertainty.
Put it right by adding bars only where uncertainty is known.
Exam tips
- Read the question carefully to see whether uncertainty is given for x, y or both before drawing.
- Use a ruler and label the bar or state its value so the examiner can see the intended uncertainty.
- Check that the bar is symmetrical about the plotted point; asymmetry suggests an arithmetic slip.
Try the lesson
The start of the Limitation of physical measurements: Represent uncertainty in a data point on a graph using error bars. lesson, made from checked teaching notes for this specification point.
Have a go first
A student plots a data point at a value of 24 on the y-axis. The uncertainty in this value is ±3. How should the error bar be drawn on the graph?
Listen
Error bars show the uncertainty attached to each plotted value. For a point (x, y), the absolute uncertainty in the dependent variable gives a vertical bar from y − Δy to y + Δy; uncertainty in the independent variable gives a horizontal bar from x − Δx to x + Δx. Draw bars with a ruler, centred on the plotted point, with caps if you wish. For example, a current of 0.50 A with uncertainty ±0.02 A is plotted as a vertical bar from 0.48 A to 0.52 A. If only one variable has a stated uncertainty, draw only that bar. Error bars let you judge whether a line of best fit is consistent with the data and whether a point is anomalous. A strong answer earns marks for these points. Identify which variable carries the stated uncertainty and whether it is the independent or dependent variable. Calculate the upper and lower limits by adding and subtracting the absolute uncertainty from the plotted value. Draw the bar centred on the point, of correct total length 2Δy or 2Δx, using a sharp pencil and ruler. Add caps or clear end markers so the extent of the uncertainty is unambiguous. A common slip: Drawing the bar from the point to one limit only, so the length represents Δy rather than 2Δy. Instead, centring the bar on the point. Exam tip: Read the question carefully to see whether uncertainty is given for x, y or both before drawing.
Key words
Say what each word means before you turn the card.
Error bars
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Absolute uncertainty
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Line of best fit
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Anomalous
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See every definition
- Error bars
- Bars drawn on a graph to show the uncertainty attached to each plotted value, centred on the plotted point.
- Absolute uncertainty
- The value added to and subtracted from a plotted value to give the upper and lower limits of a bar.
- Line of best fit
- A line whose consistency with the data can be judged using error bars.
- Anomalous
- A description of a point whose status can be judged using error bars.
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