Distinguish accuracy, precision and measurement errors
Recognise random scatter and systematic shifts, including zero error, and explain how each affects a measurement.
Section 1 · Physical quantities and units
AS Level · Cambridge International Physics 9702, 2025–2027 syllabus, Topic 1. This online sequence supports learning and practice; it does not replace supervised laboratory work, full timed assessment or human subject-teacher review.
Before you begin
- Read a number with its unit and use multiplication, division, powers and right-angled triangles.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is a random error most likely to produce?
What you will learn
- Explain random and systematic errors
- Identify and correct a zero error
- Distinguish precision from accuracy
Random and systematic errors behave differently
Random errors cause repeated readings to scatter unpredictably around a mean. Repeating a measurement and averaging can reduce the influence of random variation, although it cannot remove every limitation in the method.
A systematic error shifts readings in a consistent direction, often because of calibration, parallax from a fixed viewing position or an instrument zero error. Repeating the same flawed measurement does not remove the bias. Check calibration, the method and the instrument zero.
Accuracy is closeness; precision is repeatability
Accuracy describes how close a result is to the accepted or true value. Precision describes how closely repeated measurements agree with one another. A set of tightly clustered readings can be precise but inaccurate if a systematic offset affects all of them.
A zero error occurs when an instrument reads a non-zero value at the true zero. If a caliper reads +0.20 mm with its jaws closed, subtract 0.20 mm from each displayed reading. Apply the signed correction consistently and state it.
Pause and explain
A scale reads 0.4 g with nothing on it. What kind of error is this?
Worked example
A micrometer reads +0.03 mm when closed. It then reads 4.28 mm for a wire. Find the corrected diameter and classify the error.
Show the worked solution
- The zero reading is +0.03 mm, so the instrument has a positive zero error.
- Corrected reading = 4.28 − 0.03.
- The same offset affects every measurement, so it is systematic.
Answer 4.25 mm; a positive systematic zero error.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A balance reads −0.6 g when empty and displays 82.4 g for a sample. Find the corrected mass.
Give me a hint
Subtract the signed zero reading from the displayed reading.
Compare my reasoning
- Zero reading = −0.6 g.
- Corrected value = 82.4 − (−0.6).
- Check that correcting a negative offset increases the reading.
83.0 g.
Look for these in your work
- Signed zero error used
- Corrected mass has unit g
Three measurements are 10.1 cm, 10.2 cm and 10.1 cm. Explain what this says about precision and what it does not establish about accuracy.
Give me a hint
Compare the readings with one another, then distinguish that from comparison with a true value.
Compare my reasoning
- The readings are close together.
- Close repeat readings suggest good precision.
- No accepted value is given, so accuracy cannot be judged from this set alone.
The readings are fairly precise, but their accuracy cannot be established without a suitable accepted or true value.
Look for these in your work
- Repeatability described
- Accuracy limitation stated
A sensor gives readings clustered around 5.8 V for a source accepted as 6.0 V. Is the set precise, accurate, both or neither? Explain.
Give me a hint
Use clustering for precision and closeness to the accepted value for accuracy.
Compare my reasoning
- The close cluster indicates repeatability.
- The mean is about 0.2 V below the accepted value.
- A consistent offset is evidence of systematic bias.
The readings appear precise but not accurate: they cluster closely yet sit systematically below 6.0 V.
Look for these in your work
- Precision judged from scatter
- Accuracy judged against accepted value
- Systematic bias recognised
Common mistakes
- Claiming repeats remove a fixed zero error
- Using accuracy to mean repeatability
- Subtracting a negative zero error as though it were positive
What can you explain now?
What is a random error most likely to produce?
Compare with the explanation
Scatter among repeated readings
Random variation changes unpredictably between trials.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How can a result be precise but inaccurate, and which correction will repeated readings not remove?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.