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Random and systematic errors; accuracy and precision

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

Every measurement has errors. Knowing which kind you are dealing with tells you how to reduce it, and examiners expect the right word in your explanation.

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Key words

Pearson's practical appendix defines:

Error: the difference between a measured value and the true value. It is not a mistake.
Accuracy: how close a measurement is to the true value.
Precision: how close repeated measurements are to each other. It depends only on random effects.
Uncertainty: the interval within which the true value is expected to lie.

Random errors

Random errors make readings scatter unpredictably either side of the true value: reaction time, judging when a pendulum passes a mark, small draughts, reading between scale marks.

Reduce them by repeating and averaging, or by taking many readings and drawing a line of best fit.
They cannot be eliminated, only reduced.

Systematic errors

Systematic errors shift every reading by the same amount or proportion in the same direction: a zero error, a wrongly calibrated instrument, a delay in releasing a ball, heat losses that always make a temperature rise too small.

Repeating does not reduce them.
Reduce them by correcting for zero error, calibrating instruments against a known standard, or improving the method.
On a graph, a systematic error often shows as an intercept when the line should pass through the origin.

Putting it together

Readings can be precise but not accurate (close together, but all shifted by a systematic error), or accurate on average but not precise (large random scatter around the true value). In explanations, always link a technique to the type of error it reduces, and spell 'systematic' correctly.

Worked example

A metre rule has a worn end, so its zero is 3 mm beyond the end. A student measures six pendulum lengths from the end of the rule. What happens to the results and the graph of T² against l?

Every measured length is 3 mm too large: a systematic error.
Repeating the measurements will not remove it.
The graph of T² against l is shifted 3 mm to the right, giving an intercept on the length axis, but the gradient is unchanged.

Answer: The value of g from the gradient is still correct; the intercept reveals the systematic error

Key idea: Random errors scatter readings: repeat and average. Systematic errors shift every reading: correct, calibrate or redesign. Precise means close together; accurate means close to the true value.

Check yourself

Variations in a person's reaction time when starting a stopwatch cause which type of error?
- Systematic error
- Zero error
- Calibration error
- Random error
Show answer
Random error. Reaction time varies unpredictably from reading to reading.
A thermometer always reads 2 °C higher than the true temperature. What is this?
- A random error
- A systematic error
- A resolution error
- An anomalous reading
Show answer
A systematic error. The same shift on every reading is systematic.
A student's repeated readings are very close to each other but all far from the true value. How are they best described?
- Accurate but not precise
- Accurate and precise
- Neither accurate nor precise, and random
- Precise but not accurate
Show answer
Precise but not accurate. Close together means precise; far from the true value means inaccurate, suggesting a systematic error.
A graph that theory says should pass through the origin has a clear intercept. What does this suggest?
- A systematic error
- A random error
- Too many readings
- The wrong scale
Show answer
A systematic error. A constant offset on every reading moves the whole line, giving an intercept.
A top-pan balance reads 0.12 g with nothing on it. It then reads 25.38 g for an object. What is the corrected mass in g?
Show answer
25.26 g. Corrected = 25.38 - 0.12 = 25.26 g.
Which change reduces the effect of random errors?
- Taking more readings and averaging them
- Correcting for zero error
- Calibrating the instrument
- Using the same faulty instrument each time
Show answer
Taking more readings and averaging them. Averaging many readings reduces random scatter; the others deal with systematic errors.
Explain why repeating readings does not reduce a systematic error.
Show answer
A systematic error shifts every reading by the same amount in the same direction, so the mean is shifted by the same amount too.. Averaging only cancels errors that scatter both ways.

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Last updated 8 November 2026. Spotted a mistake? Tell us.