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Uncertainty is a measure of how confident you can be in a measurement. All measurements contain some amount of uncertainty. Let's say we measure a piece of string to be 10cm (to the nearest cm):

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Absolute uncertainty

  • The absolute uncertainty is the range of possible real values for the length of the string.
    • Length of string = 10cm ± 0.5cm
      • Our absolute uncertainty is ± 0.5cm.
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Fractional uncertainty

  • The fractional uncertainty is the absolute uncertainty divided by the measured value.
    • Fractional uncertainty = 0.5cm10cm=120\frac{0.5cm}{10cm} = \frac{1}{20}
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Percentage uncertainty

  • The percentage uncertainty is the fractional uncertainty expressed as a percentage (i.e. multiplied by 100%).
    • Percentage uncertainty = 120×100=5%\frac{1}{20} \times 100 = 5\%

Uncertainty on Graphs

The range of possible values for a measurement can be shown as a line on an uncertainty graph. We call this line an error bar. Some points on a graph might not have error bars.

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Error bars

  • Small uncertainties are shown by small error bars.
  • Large uncertainties are shown by large error bars.
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Finding the uncertainty from a graph

  • A systematic uncertainty can be spotted if the theory and the results do not match for when the independent variable is zero.
    • For example, when measuring the current in a circuit we would expect the current to be zero when the supply potential difference is zero.
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Finding the uncertainty from a graph 2

  • If there is a systematic uncertainty, this expectation would not come true.
  • We would see that the intercept of the line wasn't zero.
  • The intercept would indicate the size of the systematic error.
  • Once the systematic error has been found, we can use the graph to find an estimate for the random error.
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Using error bars

  • Error bars can be used to find the steepest and shallowest possible lines of best fit.
    • The steepest possible line of best fit will have a gradient g1.
    • The shallowest possible line of best fit will have a gradient g2.
  • The uncertainty in the measurement should then be quoted as g1+g22±g1g22\frac{g_1 + g_2}{2} \pm \frac{g_1 - g_2}{2}.

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1Measurements & Errors

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