Did you know that a balance can give almost identical readings three times in a row and still be giving you the wrong value? Consistency feels reassuring, especially when students repeat an experiment carefully. But agreement among readings is not the whole story.
Accuracy concerns closeness to a suitable reference value; precision concerns how closely repeated measurements agree under stated conditions. The practical answer is to examine both the centre of the readings and their spread, then check the instrument, units, conditions and uncertainty. A neat-looking row of numbers is not proof of accuracy.
A worked example: two balances measuring the same object
Imagine a classroom exercise with a stable reference mass of 20.0 g established using suitable equipment. Two balances measure that same object, and the readings below are entirely illustrative—not actual results from an eduKate student or a claim about a particular device.
Balance A produces 18.7 g, 18.7 g and 18.8 g. Its readings occupy a narrow range: 18.8 − 18.7 = 0.1 g. Their mean is (18.7 + 18.7 + 18.8) ÷ 3 = approximately 18.73 g. The measurements are tightly grouped, yet their centre is about 1.27 g below the 20.0 g reference.
Balance B gives 19.5 g, 20.0 g and 20.5 g. Its mean is exactly 20.0 g, but its range is 1.0 g, ten times Balance A’s range. In this small fictional example, B’s average agrees with the reference while individual readings vary more. A appears more repeatable under these conditions, but its mean disagrees with the reference.
Do not turn that demonstration into a permanent verdict about either balance. Three observations are too few to characterise an instrument fully. A trustworthy comparison would require appropriate reference uncertainty, more repetitions, controlled conditions and checks for systematic effects.
What accuracy, precision, repeatability and uncertainty mean
Accuracy: agreement with an appropriate reference
Accuracy is about how close a measurement result is to the quantity being measured, understood through an accepted or calibrated reference and the relevant uncertainty. A reference itself may have uncertainty; it should not be treated as an infallible number. The US National Institute of Standards and Technology explains that accuracy and precision are not interchangeable terms.
Precision: agreement among observations
Precision concerns the closeness of repeated results obtained under specified conditions. A precise cluster can be displaced from the reference if the instrument has a systematic offset. Conversely, scattered individual readings can sometimes average near a reference by chance.
Repeatability: consistency under nearly the same conditions
Repeatability is a particular kind of precision: the same method, observer, instrument and setting within a short period. Reproducibility asks about agreement when stated conditions change, such as a different observer or instrument. A fair experiment identifies which situation it is testing.
Uncertainty: what the recorded figure can support
No school instrument measures without limitations. Display resolution, calibration, handling and environmental effects influence what students can responsibly conclude. Recording “18.700000 g” when the display only gives one decimal place invents detail; reporting the displayed precision and stating limitations is better.
A safe, diagnosis-first checking sequence
- State the quantity and unit: mass in grams, length in centimetres, temperature in degrees Celsius, or something else.
- Look for a suitable reference, calibration check or known control. If none is available, report repeatability rather than declaring accuracy.
- Take repeated readings using the same written method; record each original reading, including unusual results.
- Calculate the range (largest minus smallest) and, where appropriate, the mean. Keep the units attached.
- Compare the results with the reference and its uncertainty, without claiming that every deviation is an instrument fault.
- Change one suspected cause at a time when safe and approved: balance zeroing, placement, timing or method consistency.
- Explain what changed after checking and which questions remain unresolved.
Why students mix the ideas up
The common misunderstanding begins when “same answer again” is treated as “correct answer.” Students may have been trained to repeat a calculation until the output matches. Measurement is different: repeating a procedure can repeat the same bias.
Ask two diagnostic questions. First: “If a thermometer shows 22.1°C, 22.1°C and 22.1°C, what do you know?” You know it is displaying the same value under those observations, not whether that value is accurate. Second: “If two thermometers disagree, what would help you decide?” Students should propose a suitable reference, calibration information and consistent conditions rather than vote for whichever reading looks familiar.
The mistakes that spoil an otherwise careful experiment
- Calling a set accurate merely because its readings match one another.
- Assuming the mean must be accurate even when the spread is large or the sample is tiny.
- Confusing instrument resolution with demonstrated accuracy: more decimal places do not guarantee truth.
- Discarding an inconvenient reading without noting an identifiable reason or a pre-agreed rule.
- Comparing instruments at different times, locations or operating conditions as though nothing changed.
- Reporting a reference value without acknowledging how it was established and what uncertainty it carries.
What a teacher can model on the board
Draw two clusters of marks along a horizontal measurement axis, with a labelled reference. In the first cluster, the marks are close to one another but far from the reference. In the second, the marks are more scattered around the reference. Ask students to describe each picture before using the words “accurate” or “precise.” This prevents vocabulary from hiding incomplete reasoning.
Then offer four new readings for an independent check. For example, 9.8 cm, 9.9 cm, 9.8 cm and 9.9 cm against a stated reference of 10.0 cm. Students should calculate the mean as 9.85 cm and the range as 0.1 cm, compare with the reference, and state that the apparent difference cannot be judged fully without reference and measurement uncertainty. They must not declare an instrument “broken” from four invented values.
For parents: a ten-minute home demonstration without specialist equipment
Use a ruler to measure a pencil’s length three times from the same starting edge. Record exactly what the scale supports. Discuss why the starting point, viewing angle and pencil placement matter. Repeat with a second adult if useful. A pencil need not have a certified true length for this activity: the first objective is to notice how consistent results depend on the method. Without an appropriate reference, describe agreement, not accuracy.
For younger children, ask simply: “Did our answers stay close?” and “How could we check what the length really is?” For older students, ask for the range, units, likely sources of variation and limitations of their conclusion. Never use a potentially hazardous experiment merely to create more dramatic variation.
A simple progression for observing learning
First, the learner sorts examples into claims about closeness to a reference and claims about agreement among readings. Next, they calculate the ranges for unfamiliar small datasets and give reasons. Finally, they independently design a sensible measurement check and state one limitation. Save dated answers at each stage. Progress is visible when explanations become more discriminating, not when the learner simply repeats the words “accuracy” and “precision.”
Frequently asked questions
Can measurements be both accurate and precise?
Yes. Repeated readings can cluster closely and agree with an appropriate reference. But the conclusion should take account of relevant uncertainties and conditions.
If an instrument is precise, should we trust it?
Not automatically. Check calibration, the measurement method and whether there is evidence of an offset or other systematic problem.
Is the smallest range always best?
Not by itself. A small range describes repeatability for that dataset, not accuracy, usefulness for the task or freedom from systematic error.
Can a class establish accuracy without knowing a reference value?
Not conclusively from repeated agreement alone. It can describe internal consistency and identify what reference or validation would still be needed.
Further reading and reference standards
The NIST explanation of accuracy, repeatability and precision gives the formal distinctions. Within eduKateSG, compare measurement resolution versus real change, visit the Education Hub and see the Clementi progression from explanation to independent checking.
The core aim
Education should give a child the confidence to say, “These results are consistent, but I still need to check whether they are right.” That distinction turns tidy practical work into honest scientific thinking.