Measurement error in repeated length readings
PhysicsMeasurement & UncertaintyAges 15–16Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Measurement & Uncertainty
A ruler with an adjustable resolution measures a metal rod repeatedly; each reading appears half a second apart with a zoomed-in view of the scale. Random error scatters the readings around a value, while systematic error shifts the whole cluster away from the true value. The program computes the mean, each reading's absolute deviation, the mean absolute deviation, and adds the instrument error to get the measurement's absolute error, then reports the result as x̄ ± Δx together with the relative error as a percentage.
Lesson: Error in measuring a physical quantity
What it shows
No measurement is exact. Random errors, such as small slips in reading a scale, scatter repeated readings on both sides of a value, so averaging many readings gives a more reliable mean. Systematic errors, such as a ruler whose zero mark is offset, shift every reading in the same direction and cannot be reduced by repeating the measurement. The instrument error is usually taken as half the smallest scale division. Comparing the mean with the known true length shows the difference between precision (how closely readings agree) and accuracy (how close they are to the true value).
How to use
Start with the 1 mm ruler, a few readings and some zero offset. Press Measure N again and watch the readings appear one by one, then compare the mean with the true value. Increase Number of readings and notice that the mean settles but the offset remains. Next set Systematic error (zero-offset ruler) to 0 and vary Random reading fluctuation, and finally compare the Ruler resolution options of 1 mm, 0.5 mm and 0.1 mm.
Parameters you can change
- Ruler resolution 1 mm (ruler), 0.5 mm, 0.1 mm (caliper)
- Number of readings 3–20 times
- True length of the rod 50–200 mm
- Systematic error (zero-offset ruler) -2–2 mm
- Random reading fluctuation 0–2 mm
Questions to explore
- Why does taking more readings not remove a systematic error?
- How does the instrument error change when the 1 mm ruler is replaced by the 0.1 mm caliper?
- How could you detect a zero offset on a ruler before starting to measure?
