Distinguish accuracy, precision and measurement errors
Recognise random scatter and systematic shifts, including zero error, and explain how each affects a measurement.
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.
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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.