Error bars are drawn on plotted points to show the uncertainty in each measurement
Measurements & Uncertainties - OCR A-Level Physics
- Error barsLines drawn on plotted data points showing the range of uncertainty in the measurement. are drawn on plotted points to show the uncertainty in each measurement.
- Vertical error bars show uncertainty in the y-variable. Horizontal error bars show uncertainty in the x-variable.
- The length of each error $bar = 2 x absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading. (extends equally above$ and below the point).
- Draw the best-fit lineA straight line or curve drawn through data points that best represents the overall trend, minimising the total distance from all points. through as many error bars as possible.
- Draw worst linesLines of maximum and minimum gradient that still pass through all error bars; used to find the uncertainty in the gradient. (steepest and shallowest) that still pass through all 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: $uncertainty = (max$ intercept - 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.