MEASUREMENT ERRORS IN SCIENCE: HOW TO IMPROVE DATA

Published: Aug-2026 | Category: Secondary Science

What makes a measurement trustworthy? It is tempting to think that more decimal places, a larger set of readings or a smoother graph must mean better science. In reality, reliable data begins much earlier: with a clear question, suitable equipment and a method designed to control the most important sources of error.

Measurement error does not automatically mean that somebody has made a mistake. Every practical measurement has limitations. The aim is to recognise those limitations, reduce their effect where possible and decide whether the evidence is strong enough to support a conclusion.

What students can learn

This topic helps students learn how to:

• distinguish between accuracy, precision and resolution;
• identify possible sources of systematic and random error;
• choose equipment that suits the question being investigated;
• improve repeatability through a consistent method;
• use the mean, range, standard deviation and standard error to interpret repeated measurements;
• use a graph and line of best fit to investigate relationships between variables; and
• judge whether the data supports a reliable conclusion.

Start with the question

Before selecting a sensor or taking a reading, ask two questions: What am I trying to measure? and How accurately do I need to measure it?

The answers affect the equipment, measurement range, resolution, sensor position and method of data collection. A setup that works well for a large temperature change may not be suitable when the expected change is only a fraction of a degree.

This is why a high-resolution instrument cannot rescue a poorly designed investigation. It may display very small changes, but those changes will not be useful if the sensor is in the wrong place or the experiment does not answer the original question.

Where can measurement error come from?

Useful checks include:

• Equipment: Is the instrument suitable for the quantity and conditions being measured?
• Resolution: Can it distinguish the smallest change that matters?
• Accuracy: How close is the reading expected to be to the true value?
• Calibration: Could the instrument consistently read too high or too low?
• Placement: Is the sensor measuring the intended location or condition?
• Environment: Could temperature, movement, sunlight or another factor affect the result?
• Response time: Can the instrument respond quickly enough as conditions change?
• Repeatability: Do repeated measurements give similar results?
• Sampling: Do the readings represent the process being studied?
• Human factors: Could handling, reading or recording introduce variation?

Accuracy, precision and resolution

These terms describe different features of a measurement:

• Accuracy is how close a measurement is to the true value.
• Precision, or repeatability, is how close repeated measurements are to one another.
• Resolution is the smallest change that an instrument can distinguish.

A set of readings may be close together but still be wrong if the instrument has a consistent bias. In that case the measurements are precise but not accurate. Equally, readings may be spread out around the true value: accurate overall, but not very precise.

Resolution also needs careful interpretation. A display with more decimal places does not necessarily provide a more accurate answer. Those digits are only useful when the instrument's accuracy, calibration and measurement method are good enough to support them.

Systematic and random error

Systematic error shifts measurements consistently in one direction. Possible causes include a zero error, poor calibration, incorrect setup, a consistent environmental effect or measuring in the wrong position.

Where possible, compare the equipment with a known reference and ask: is something causing all the readings to be too high or too low? Simply taking more measurements will not remove a systematic error.

Random error causes repeated measurements to vary unpredictably. Its effect can often be reduced or described by repeating measurements, keeping the procedure consistent, controlling environmental conditions and collecting enough good-quality data to calculate a mean and spread.

A practical measurement checklist

Before collecting data, students can work through this sequence:

1. Write a clear question and identify the variables.
2. Estimate the values or changes likely to occur.
3. Select equipment with a suitable range, resolution and accuracy.
4. Check the calibration or compare the instrument with a known reference.
5. Position the sensor so that it measures the intended condition.
6. Keep the surroundings and method as consistent as possible.
7. Choose a sampling approach that captures the process without overlooking important changes.
8. Repeat the measurement when appropriate.
9. Inspect the data for patterns, variation and unexpected results.
10. Use suitable statistics before drawing a conclusion.

When collecting readings with EasySense, this thinking should happen before recording begins. Students can then examine the resulting data or graph and ask whether the pattern is likely to be real, whether the readings are repeatable and whether the setup may have introduced bias.

Using statistics to understand repeated measurements

A single average cannot describe everything about a set of results. Several simple statistics help reveal both the typical value and the amount of variation.

Mean

The mean is the total of all the readings divided by the number of readings. It gives a typical value for the set:

Mean = sum of readings ÷ number of readings

Range

The range is the difference between the largest and smallest values:

Range = maximum value − minimum value

It is a quick measure of overall spread, although it depends only on the two most extreme readings.

Standard deviation

Standard deviation describes how spread out the measurements are around the mean. A small standard deviation means the readings tend to be close to the mean; a larger value indicates greater variation.

Standard error

Standard error describes the precision of the estimated mean. It is calculated by dividing the standard deviation by the square root of the number of readings:

Standard error = standard deviation ÷ √number of readings

As the number of suitable measurements increases, the standard error will generally decrease. This can improve confidence in the estimated mean, but it still will not correct a systematic bias.

Worked example

Suppose five temperature readings are 20.1, 20.4, 19.9, 20.2 and 20.4 °C.

• Mean: 20.2 °C
• Range: 0.5 °C
• Standard deviation: 0.21 °C
• Standard error: 0.09 °C

The mean gives the typical measurement. The standard deviation describes the variation between the individual readings, while the standard error describes the precision of the estimated mean. Together, they provide a more useful account of the data than the mean alone.

Investigating relationships with graphs

When an investigation asks whether two variables are related, plot the measurements and look for a pattern. A line of best fit can summarise a linear relationship using:

y = mx + c

Here, m is the gradient and c is the intercept. The least-squares method finds the line that minimises the total squared difference between the measured points and the fitted line. The model can then help describe the relationship and, within sensible limits, make predictions.

The coefficient of determination, written as R², indicates how closely the data fits the model. An R² value close to 1 indicates a stronger fit, while a value close to 0 indicates a weak fit. For example, R² = 0.90 means that the model accounts for 90% of the variation in the response variable.

A strong fit does not by itself prove that one variable causes the other. Students should still consider the method, possible errors, the range of data collected and whether a different model may be more suitable.

Ideas for classroom investigation

• Compare repeated temperature readings taken with different sensor positions.
• Investigate how changing the recording interval affects the detail visible in a graph.
• Introduce a deliberate zero offset and ask students to identify the resulting systematic error.
• Compare two sets of readings with similar means but different spreads.
• Ask students to improve an unreliable method, then explain which sources of error their changes address.
• Fit a straight line to paired measurements and discuss what the gradient, intercept and R² value reveal.

Better measurements lead to better conclusions

Good measurement is a complete chain: question, equipment, calibration, range, resolution, accuracy, placement, conditions, sampling, repeatability, statistics and conclusion. A weakness at any stage can limit the quality of the final evidence.

Reducing error is not about always choosing the most sophisticated equipment. It is about selecting an appropriate method, controlling the important variables, collecting enough good-quality measurements and using statistics to understand what the data is showing.

Download the full activity

The full worksheet includes an equipment checklist, explanations of systematic and random error, statistical formulae, a worked temperature example and guidance on lines of best fit.

Find and download the worksheet in Practical Explorer