Experimental uncertainty

Also called Measurement uncertainty, Error bars

Experimental uncertainty is the range within which a measured value plausibly lies, reported as a value plus or minus a range. It is a property of the measurement itself, not evidence that somebody made a mistake.

The AP Physics 1 CED puts it to teachers directly: students need to understand that scientific instruments do not produce exact measurements, and to learn what steps reduce uncertainty. A result of 1.42±0.03 s1.42 \pm 0.03\ \text{s} is a complete answer. A result of 1.42 s1.42\ \text{s} with no range is an incomplete one.

Reading it off an instrument:

  • An analogue scale is usually quoted to half its smallest division, so a metre rule marked in millimetres gives about ±0.5 mm\pm 0.5\ \text{mm}.
  • A digital display is usually quoted to one unit in its last digit.
  • Repeating a measurement and spreading the results gives you a better estimate than either.

Random uncertainty scatters readings either side of the true value, and averaging repeated trials shrinks it. Systematic error shifts every reading the same way, from a scale that does not zero or a stopwatch started late, and repeating will never remove it. Only the first kind is what error bars on a graph show.

The exam pays for this. In the AP Physics 1 sample Experimental Design and Analysis question, one of the ten points goes purely to describing a reasonable method of reducing experimental uncertainty, in that case by taking pressure readings at several depths rather than one.

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