Every measurement has some uncertainty. Random errors make repeats scatter unpredictably, for example reaction time when using a stopwatch; repeating and averaging reduces their effect. Systematic errors shift every result by the same amount in the same direction, such as a balance that reads 2 g too high or a zero error on a meter; repeating does not remove them, so instruments must be checked and calibrated.
Uncertainty can be estimated as half the range of the repeats. A measurement of 3.2 ± 0.1 cm is more precise than 3.2 ± 0.5 cm. Accuracy is how close a result is to the true value; precision is how close the repeats are to each other.
Worked example
A thermometer always reads 1 °C too high. Is this a random or a systematic error?
- The error is the same every time and in the same direction.
- Repeating will not cancel it out.
Answer:It is a systematic error; calibrate or correct the readings.
Key words
- random error
- unpredictable scatter between repeats
- systematic error
- the same shift in every reading
- zero error
- a meter not reading zero when it should
- calibrate
- check an instrument against a known value
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