Errors, Precision & Accuracy
Errors, Precision & Accuracy
- Measurements can differ from the true value in two patterns, 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 biases readings in a consistent direction. A zero error may add the same amount each time; a badly calibrated meter may make every reading a fixed percentage too high.
- A makes repeated readings vary unpredictably. Some readings are high and some are low, for example when a scale is judged by eye.
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- 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 turn9702/11/O/N/21 Q5 · 1 mark · adapted
Classify the errors: (1) a meter read from different angles, (2) a meter that always reads 5% high, (3) a needle that sometimes sticks, and (4) a zero error.
Show worked answer
Random: (1) and (3). Systematic: (2) and (4). Ask whether repeated readings vary unpredictably or remain biased in a consistent direction.
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.
- A systematic error usually reduces accuracy because the result remains biased. Random error reduces precision because repeated readings spread out; averaging can reduce its effect on the mean.
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.