Errors, Precision & Accuracy
Errors, Precision & Accuracy
- Real measurements go wrong in two different ways, and the exam asks you to tell them apart.
- The same two ideas give the exam words precision and accuracy, which do not mean the same thing.
Systematic and random errors
- A shifts every reading the same way: a zero error, or a meter that always reads 5% high.
- A scatters readings on both sides of the true value: judging by eye, or a needle that sometimes sticks.
- Random error is reduced by repeating and averaging: the high and low readings partly cancel.
- Systematic error is not reduced by averaging, because every reading is shifted the same way. Fix it by re-calibrating the instrument or subtracting the zero error.
Your turn— tap to reveal the worked answer (9702/11/O/N/21 Q5)
Classify each source of error: (1) a meter read from different angles, (2) a meter that always reads 5% too high, (3) a needle that sometimes sticks, (4) a meter with a zero error. (9702/11/O/N/21 Q5)
Answer: random: (1) and (3). Systematic: (2) and (4). The test is one question: does the error shift every reading the same way?
Averaging reduces random scatter. It does not remove a systematic error, so the mean is still shifted from the true value.
Precision and accuracy
- : how closely repeated readings agree with each other.
- : how close the readings are to the true value.
- The two are independent. A set of readings can be precise but not accurate, or accurate but not precise.
- Link to the last section: a systematic error makes results less accurate (all shifted). A random error makes them less precise (spread out).
Worked example
High precision, low accuracy
Four students each measure (true value 9.81 m s⁻²) three times. Which set has high precision but low accuracy?
- Set D reads 10.1, 10.2, 10.1. The readings are very close to each other, so precision is high.
- But the mean, about 10.1, is far from 9.81, so accuracy is low.
Answer
(9702/11/M/J/25 Q2)
Common mistake
Precise does not mean accurate. A micrometer with a zero error gives repeatable readings that are all wrong: high precision, low accuracy.