Measurement errors fall into two categories: systematic errors, which shift all measurements in the same direction, and random errors, which vary unpredictably around the true value. Identifying them is essential for improving measurement quality.
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How to measure it in class
With the FizziQ app, it is possible to demonstrate these two types of errors.
Steps:
- Repeat a measurement (for example, the period of a pendulum) 10 times
- Observe the spread of results → random errors
- Compare the average obtained to the theoretical value
- If the deviation is significant and constant → likely systematic error
- Identify possible causes (calibration, method, environment)
- Correct the systematic error if possible, reduce random errors by averaging
Scientific activities on this topic
Possible extensions with FizziQ: critical analysis of a series of measurements, comparison of two methods for the same result, and checking a sensor against a known reference value (g, standard frequencies) to reveal a possible bias.
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Comparison:
| Characteristic | Systematic error | Random error |
|---|---|---|
| Direction | Always the same direction | Variable |
| Effect on the average | Shifts it | Cancels out (large n) |
| Reduction | Correction, calibration | Repetition, averaging |
| Detection | Comparison to a reference | Spread of measurements |
Sources of systematic errors:
- Poorly calibrated instrument (offset zero)
- Parallax error (always reading from the same side)
- Biased method (operator reaction time)
- Uncorrected non-ideal conditions (temperature)
Sources of random errors:
- Instrument fluctuations
- Variations in conditions (vibrations, air currents)
- Imprecise reading (variable interpolation)
- Electronic noise from sensors
Graphical representation:
A series of shots at a target illustrates this well:
- Precision (low random errors) → grouped shots
- Trueness (low systematic error) → centered shots
- Accuracy = precision + trueness
Formula
Random error (estimated by the standard deviation): σ = √[Σ(xᵢ - x̄)²/(n-1)]
The random error on the average decreases with n: σ_average = σ/√n
The systematic error does not depend on n: x̄ = μ + systematic_error
Application examples
- A stopwatch that systematically starts 0.1 s late → systematic error
- Variations in the operator’s reflexes → random error
- A poorly tared scale → systematic error
- Micro-vibrations of the floor → random error
FAQ
Q: How do I know if I have a systematic error? A: Compare your average result to a reference value. If the deviation is clearly larger than the statistical uncertainty, there is probably a systematic error.
Q: Can random errors be eliminated? A: No, but they can be reduced by taking more measurements. The uncertainty on the average decreases as 1/√n.
Q: Does FizziQ help detect systematic errors? A: By comparing FizziQ measurements to known values (g, reference frequencies), a sensor bias can be detected.
Q: Which error is more serious? A: Systematic errors, because they do not compensate for each other and can go unnoticed. Random errors are visible and average out.
Related concepts
Measurement Uncertainty - Calibration - Precision - Reproducibility