fundamentals · 5 min read
Accuracy vs precision: what the difference means for data
Accuracy asks whether a measurement is close to the true value; precision asks whether repeating it gives the same answer. The two are independent, and a result can be precise without being accurate, which is why a tight cluster of readings is not proof that an instrument is right.
This comparison defines both terms, describes the classic target analogy in words, and connects each idea to a number you can report: percent error for accuracy, standard deviation for precision, and significant figures for the resolution of what you write down.
The classic target, described in words
Imagine arrows aimed at a target. Clustered tightly at the edge: precise but not accurate, because the throws were repeatable while the aim is offset. Scattered widely around the centre: accurate on average but not precise, because the throws average to the middle without being repeatable. Tightly clustered in the centre: both. Scattered widely and off-centre: neither.
The key phrase is on average for the scattered throws: their centre can be near the true value while individual measurements are far from it. An instrument can also be precise and biased in a stable way, so repeated readings agree with each other and share the same systematic error.
Precision has two parts: repeatability and resolution
Repeatability is how closely repeated measurements of the same quantity agree; it is what a standard deviation or range summarises. Resolution is the smallest change an instrument can display or distinguish, such as the last digit on a digital readout. They are related but not interchangeable: a display with many digits can still give scattered readings.
High resolution can create a false impression of high precision when the last digits wander. Repeating the measurement is the only way to see the difference, and reporting more digits than the repeats justify overstates the precision.
Where accuracy and precision appear in the numbers
Accuracy is checked against a reference: percent error compares the measured value with an accepted one, and a calibration checks whether an instrument responds correctly across a range. Precision is checked by repeated measurements: the standard deviation and the range describe how much independent readings vary.
Significant figures describe reported resolution rather than either concept directly. A number with four significant figures claims more resolution than one with two, but that claim is only justified if the instrument and repeats support it. A calibration curve links the two ideas: scatter around the fitted line reflects precision, while a slope or intercept shifted by a bad standard reflects accuracy.
A biased instrument can be very precise
A balance that consistently reads half a gram high demonstrates the difference. Repeating the same weighing gives values that agree to the last digit, so the precision looks excellent and the standard deviation is tiny, yet every reading is wrong by the same amount. Repeating the measurement cannot reveal the bias, because the error is systematic rather than random.
Only a reference exposes the offset: a calibrated mass, a certified standard, an independent method or a blank. Random error shrinks with averaging; systematic error does not, so it has to be found and corrected through calibration or procedure.
Put numbers on the balance example: a certified 10.00 g mass reads 10.48, 10.50 and 10.52 g on three repeat weighings. The spread is small — the standard deviation is around 0.02 g — so the instrument is precise, yet every reading is about 5% high, so its accuracy is poor. The repeatability hid a constant offset that only the reference mass exposed.
Reporting both without overclaiming
A complete result pairs the measured value with an uncertainty and a statement about accuracy where a reference exists. Give the value, its unit, the number of repeats and the standard deviation or standard error, labelled, plus percent error against a reference if one is available. State the calibration source if traceability matters.
Avoid the two common shortcuts: quoting many significant figures and assuming precision, or reporting a tight standard deviation and assuming accuracy. Round the number to the resolution the instrument and repeats support, and keep the accuracy check separate from the precision estimate so a reader can see which was measured.
Keep the vocabulary consistent from the method to the results table and the discussion: switching between error, uncertainty and standard deviation without defining each term leaves readers guessing which quantity is being reported.
- Repeat the measurement before claiming precision.
- Compare with a reference before claiming accuracy.
- Label every uncertainty as standard deviation, standard error or tolerance.
- Do not report more digits than the instrument and repeats support.
- Report accuracy and precision separately, with the method stated.