Error bars are drawn on plotted points to show the uncertainty in each measurement
Measurements & Uncertainties - OCR A-Level Physics
Diagram pending
Graph of current vs voltage. Six plotted points, each with vertical error bars of ±0.6 A and horizontal error bars of ±0.03 V. A straight line of best fit passes through or near every error-bar box. Axes labelled V/V and I/A.
Will be replaced with a GeoGebra SVG in stream 2.
Key Definition
Error bars
Short lines drawn through each plotted point on a graph showing the absolute uncertainty in that reading. They extend equally above and below the point for vertical uncertainty, and left and right for horizontal uncertainty. A vertical error bar represents uncertainty in the $y$-variable; a horizontal one represents uncertainty in the $x$-variable. The total length of an error bar is twice the absolute uncertainty.
Short lines drawn through each plotted point on a graph showing the absolute uncertainty in that reading. They extend equally above and below the point for vertical uncertainty, and left and right for horizontal uncertainty. A vertical error bar represents uncertainty in the $y$-variable; a horizontal one represents uncertainty in the $x$-variable. The total length of an error bar is twice the absolute uncertainty.
Line of best fit
Line of best fit
A single straight line (or smooth curve) drawn through the data that minimises the total distance from all points and passes through as many error bars as possible. The gradient and intercept of this line are used to extract physical quantities.
A single straight line (or smooth curve) drawn through the data that minimises the total distance from all points and passes through as many error bars as possible. The gradient and intercept of this line are used to extract physical quantities.
- Total length of each error bar $= 2 \times \Delta x$ (the absolute uncertainty in that reading).
- Draw the line of best fit through as many error bars as possible. It does not have to touch every point.
- To find the uncertainty in the gradient, also draw the two worst acceptable linesThe steepest and shallowest lines that still pass through every error bar. The spread between them gives the uncertainty in the gradient.: steepest and shallowest, both still consistent with the error bars.
$$\text{Uncertainty in gradient} = \frac{\text{steepest gradient} - \text{shallowest gradient}}{2}$$
$$\text{Percentage uncertainty in gradient} = \frac{\text{uncertainty in gradient}}{\text{best-fit gradient}} \times 100\%$$
- The same method applies to the $y$-intercept: $\Delta(\text{intercept}) = \frac{\text{max intercept} - \text{min intercept}}{2}$.
- If the question gives you a theoretical value, compare your gradient to it and calculate the percentage difference.
- If the percentage difference is within your percentage uncertainty, the result is consistent with theory.
Common Mistake
MEDIUM
Wrong: Drawing worst lines that do not pass through any error bars.
Right: Worst lines must pass through the error bars. The steepest line should go through the top of the first error bar and bottom of the last (or vice versa). They define the range of possible gradients.
Right: Worst lines must pass through the error bars. The steepest line should go through the top of the first error bar and bottom of the last (or vice versa). They define the range of possible gradients.
Examiner Tips and Tricks
- When asked for the uncertainty in a gradient, examiners expect to see worst lines drawn on your graph.
- If there are no worst lines, you will score zero for this part.
- Always draw them, even if the question does not explicitly ask.