Accuracy, Precision and Repeated Trials
In 2018, Australian Olympic shooter Elena Galiabovitch fired 60 shots within a 10 cm circle at 10 m — precise but 3 cm off the bullseye, costing her a medal.
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Three students measure the boiling point of water. Student A gets 98, 102 and 100 degrees. Student B gets 99.8, 99.9 and 100.1 degrees. Student C gets 95, 95 and 95 degrees.
Which student is accurate? Which is precise? Which is both, and which is neither? How do you know?
Weigh a 100 g calibrated mass on your school balance five times. You get 98.2, 98.3, 98.1, 98.2, 98.3 grams — impressively consistent, but all nearly 2 g below the real value. Your results are repeatable, but they are all wrong in the same direction. That is the difference between accuracy and precision. Accuracy describes how close a measurement is to the true or accepted value. An accurate measurement is correct, even if it is only taken once. Accuracy depends on the quality of your instrument, your technique, and whether your method has any built-in bias.
Think of accuracy like an archer aiming at a target. If the arrows cluster around the bullseye, the archer is accurate. If the arrows cluster far from the centre, the archer is inaccurate — even if the cluster is tight. In science, accuracy is essential because decisions and conclusions depend on measurements being trustworthy representations of reality.
Accuracy is not about how many times you measure. A single accurate reading is more valuable than a hundred inaccurate ones.
A scientist measures the melting point of ice as 0.1 degrees Celsius. This is highly accurate because it is very close to the true melting point of 0 degrees. A reading of 5 degrees would be inaccurate.
Geoscience Australia maintains reference standards for mineral analysis. When mining companies assay gold samples, accuracy matters enormously — a small systematic error could misvalue a deposit by millions of dollars.
Many students confuse accuracy with precision. They think that because a measurement is repeated many times, it must be accurate. This is wrong. A biased instrument can give the same wrong answer every single time.
Precision describes how close repeated measurements are to each other. A precise instrument gives very similar readings every time you use it, even if those readings are all wrong. Precision is about consistency and repeatability, not about being correct.
Returning to the archer analogy: if all arrows land tightly clustered in one corner of the target, the archer is precise but inaccurate. The shots are repeatable, but they miss the mark. In a laboratory, a precise but inaccurate balance might read 10.2 g, 10.2 g and 10.2 g for a true 10.0 g mass. It is perfectly consistent, but consistently wrong.
Precision is valuable because it tells you that your method is stable and your equipment is reliable. Once you have precision, you can work on correcting any systematic bias to achieve accuracy.
A student measures the volume of water three times and gets 24.5 mL, 24.6 mL and 24.5 mL. These results are highly precise because they are very close together. If the true volume is 30 mL, they are precise but inaccurate.
The Australian Synchrotron produces X-ray beams of extraordinary precision for materials research. Scientists use these beams to measure atomic structures with repeatability that supports world-leading discoveries in medicine and engineering.
Students often say a measurement is 'precise' when they mean it is 'correct.' Precision has nothing to do with correctness. A broken clock is precise — it shows the same wrong time every day — but it is never accurate.
Accuracy and precision are independent qualities. A measurement can be accurate but imprecise, precise but inaccurate, both, or neither. Understanding this distinction is one of the most important skills in experimental science.
Accurate and precise means your measurements cluster tightly around the true value — the ideal situation. Precise but inaccurate means tight clustering away from the true value, usually caused by systematic error. Accurate but imprecise means your measurements scatter widely but average close to the true value — random error dominates. Neither accurate nor precise means scattered measurements that are also far from the truth — the worst-case scenario requiring major method improvements.
Scientists aim for accuracy and precision, but when they cannot have both, they diagnose which type of error is causing the problem and fix it systematically.
Four students measure a 50.0 g mass: Student A gets 49.8, 50.2, 49.9 (accurate, imprecise). Student B gets 52.1, 52.2, 52.1 (precise, inaccurate). Student C gets 50.0, 50.0, 50.0 (both). Student D gets 47, 53, 49 (neither).
BOM weather stations across Australia are calibrated for both accuracy and precision. A station that reads consistently 2 degrees high is precise but inaccurate; a station that jumps randomly between correct and wrong is accurate on average but imprecise. Both problems must be fixed for reliable forecasting.
Many students believe accuracy and precision are just different words for 'correct.' This is wrong. They describe completely different things: accuracy is about distance from truth, precision is about distance between repeated measurements.
Complete this description of a measurement.
Wrong: Accuracy and precision mean the same thing.
Right: Accuracy is about being correct. Precision is about being consistent. You can be precise but inaccurate, or accurate on average but imprecise.
Wrong: One good measurement is enough if you are careful.
Right: Even careful scientists make random errors. Repeating trials and averaging reduces the impact of these unpredictable variations.
Wrong: Using accuracy and precision interchangeably.
Right: Accuracy is about correctness relative to a true value. Precision is about consistency between repeats. Keep these distinct when discussing your results.
Wrong: Doing only one trial to save time.
Right: A single measurement could be affected by a random error. You have no way of knowing if it is representative. Always do at least three trials where possible.
Repeating a measurement multiple times is one of the simplest and most powerful techniques in science. A single measurement might be affected by a momentary distraction, a gust of air, or a slight misread of a scale. By taking several trials and calculating the mean, scientists reduce the impact of these random fluctuations.
The mean is not the only benefit. Repeated trials also let you calculate the range — the difference between the highest and lowest values — which tells you how spread out your data is. A small range means high precision. A large range means you need to improve your technique or equipment. Together, the mean and range give a much clearer picture than any single measurement could provide.
However, repeated trials cannot fix systematic errors. If your ruler is worn, all ten measurements will be wrong in the same way. Repetition fixes randomness, not bias.
A student measures reaction time five times and gets 0.24, 0.31, 0.26, 0.29 and 0.25 seconds. The mean is 0.27 s and the range is 0.07 s. The single value of 0.31 s looks odd alone, but the mean shows it is just part of normal variation.
The Australian Institute of Sport uses repeated trials to assess athlete performance. A single unusually fast sprint might be wind-assisted; the mean of multiple trials gives coaches a reliable picture of true ability, while the range reveals consistency.
Students often think one perfect measurement is better than several good ones. This is wrong. Even expert scientists make random errors. Repeating trials is not a sign of weakness — it is a sign of scientific rigour.
Speed Round · 6 questions
True or false? Tap as fast as you can. Build a streak.
Accuracy refers to how close repeated measurements are to each other.
Precision refers to how close repeated measurements are to each other.
You can be precise but inaccurate.
Repeating a measurement only once is enough if you are careful.
The mean of repeated trials is usually more reliable than any single measurement.
High precision guarantees that a measurement is correct.
How are you completing this lesson?
At the start of the lesson you were asked: "A scale always reads 0.5g less than the true mass — is it accurate? Is it precise?" Think about how you would have answered that before this lesson.
Now that you know the difference between accuracy and precision, you should be able to answer confidently. Which quality is affected by the consistent 0.5g error? Could the scale still be useful in any situation, and why?
Evaluate each student's results in terms of accuracy and precision, and suggest one specific improvement each student could make.
Quick Check · 5 questions
Check Your Understanding · 3 questions
1. A student measures a 50 gram mass three times and gets 48, 52 and 50 grams. Another gets 47, 47 and 47 grams. Compare their accuracy and precision.
2. Why is it possible to be precise but inaccurate? Give a real-world example.
3. Explain how repeating trials three times and calculating the mean improves the reliability of your data.
Show Your Working · 3 questions
SA1. Distinguish between accuracy and precision, using a real-world or experimental example to illustrate a situation that is precise but not accurate. (4 marks)
SA2. Explain why a single measurement is less reliable than the mean of three repeated measurements, referring to random error in your answer. (4 marks)
Hint: Think about how random errors affect individual measurements differently.
SA3. A set of measurements is both accurate and precise. Describe what this would look like on a target diagram and in a data table. (3 marks)
Quick Check
1. B — Precision is about consistency between repeated measurements.
2. B — The results are tightly clustered (precise) but consistently above the true value (not accurate).
3. B — Repeating trials reduces the effect of random errors.
4. B — Scattered around the true value means accurate on average but imprecise.
5. B — High precision shows the method is consistent and repeatable.
Show Your Working Model Answers
SA1 (4 marks): Accuracy is how close a measurement is to the true value [1]. Precision is how close repeated measurements are to each other [1]. Example: a clock that is always 5 minutes slow shows the same wrong time every day (precise) but never the correct time (inaccurate) [2].
SA2 (4 marks): A single measurement may be affected by a random error [1]. You cannot tell if it is representative [1]. Three measurements allow you to see variation [1]. The mean reduces the impact of random errors because positive and negative variations partially cancel out [1].
SA3 (3 marks): On a target diagram, the darts would be clustered tightly around the bullseye [1]. In a data table, the values would be close to each other and close to the true value [1]. Both accuracy and precision are high [1].
Accuracy
How close to the true value
Precision
How close repeats are to each other
Repeatability
Consistent results under same conditions
Mean
Average of a set of values
Reliability
Consistency across repeated trials
Random error
Unpredictable variation in measurements
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