Introduction

Scientists rarely obtain the exact same measurement every time they perform an experiment. Small differences naturally occur because of limitations in measuring instruments, experimental techniques, and environmental conditions.

When evaluating measurements, scientists consider two important ideas:

• Accuracy – How close a measurement is to the true or accepted value.
• Precision – How close repeated measurements are to one another.

Understanding the difference between these two concepts is essential for designing reliable experiments and interpreting scientific data.

 

 

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What is Accuracy?

Accuracy describes how close a measurement is to the true or accepted value.

The closer the measurement is to the correct value, the more accurate it is.

Example

Suppose the true length of a metal rod is 25.0 cm.

A student measures:

• 24.9 cm

This measurement is very accurate because it is close to the true value.

What is Precision?

Precision describes how close repeated measurements are to each other.

If repeated measurements are very similar, they are considered precise.

Precision is about consistency, not necessarily correctness.

Example

A student measures the same object five times:

• 18.2 cm
• 18.2 cm
• 18.1 cm
• 18.2 cm
• 18.1 cm

These measurements are highly precise because they are very close together.

Accuracy vs Precision

Accuracy and precision are not the same thing.

A set of measurements may be:

• Accurate and precise
• Accurate but not precise
• Precise but not accurate
• Neither accurate nor precise

The following target diagrams help illustrate these possibilities.

 

 

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Examples of Accuracy and Precision

Suppose the true mass of an object is 100.0 g.

Example A

Measurements:

• 99.9 g
• 100.0 g
• 100.1 g

These measurements are:

• Accurate
• Precise

Example B

Measurements:

• 94.8 g
• 94.9 g
• 94.8 g

These measurements are:

• Precise
• Not accurate

Example C

Measurements:

• 98.5 g
• 101.2 g
• 100.3 g

These measurements average close to the true value but vary considerably.

They are:

• Fairly accurate
• Not very precise

Sources of Error

Measurements are affected by experimental errors.

Errors do not necessarily mean mistakes have been made.

Instead, they refer to factors that cause measurements to differ from the true value.

The two main types are:

• Systematic errors
• Random errors

Systematic Errors

A systematic error affects every measurement in the same way.

It shifts all measurements in one direction.

Common causes include:

• A balance that always reads 0.5 g too high.
• A ruler with a worn or damaged zero mark.
• A thermometer that has not been calibrated correctly.

Systematic errors mainly reduce accuracy.

 

 

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Random Errors

A random error causes small, unpredictable differences between measurements.

Examples include:

• Slight reaction time differences when using a stopwatch.
• Reading a scale from slightly different angles.
• Small temperature changes during an experiment.
• Tiny vibrations in laboratory equipment.

Random errors mainly reduce precision.

Comparing Systematic and Random Errors

Evaluating Experimental Data

Scientists examine both accuracy and precision when evaluating results.

Good experimental data should be:

• Close to the accepted value.
• Consistent when repeated.

Neither accuracy nor precision alone is sufficient.

Reliable scientific measurements require both.

Improving Accuracy

Accuracy can often be improved by:

• Calibrating measuring instruments.
• Using higher-quality equipment.
• Checking for zero errors.
• Following correct measuring techniques.
• Avoiding parallax error when reading scales.

Improving Precision

Precision can often be improved by:

• Repeating measurements several times.
• Calculating the average (mean) result.
• Using instruments with finer scale divisions.
• Keeping experimental conditions consistent.
• Measuring carefully using the same technique each time.

 

 

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Real-World Applications

Accuracy and precision are essential in many professions.

 

 

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Examples include:

• Medical laboratories
• Pharmaceutical manufacturing
• Engineering
• Construction
• Space exploration
• Scientific research
• Environmental monitoring
• Quality control in manufacturing

Small measurement errors can have serious consequences, making accurate and precise measurements essential.

Worked Examples

Example 1

The accepted mass of an object is 50.0 g.

A student records:

• 50.1 g
• 50.0 g
• 49.9 g

Answer:

The measurements are both accurate and precise.

Example 2

A balance always reads 0.4 g too high.

What type of error is this?

Answer:

A systematic error.

Example 3

A student records:

• 32.1 cm
• 31.7 cm
• 32.4 cm
• 31.9 cm

The measurements are spread out.

Answer:

The measurements have low precision.

Example 4

How can precision be improved?

Answer:

Repeat the measurements several times and calculate the average.

Example 5

How can accuracy be improved?

Answer:

Calibrate measuring instruments and use correct measuring techniques.

Did You Know?

Modern scientific laboratories often use instruments capable of measuring extremely small differences. For example, analytical balances can measure masses to 0.0001 g (0.1 mg), allowing scientists to detect tiny changes that would be impossible to observe with ordinary classroom equipment.

Key Terms

Key Takeaways

• Accuracy describes how close a measurement is to the true value.
• Precision describes how consistent repeated measurements are.
• Measurements can be accurate without being precise, or precise without being accurate.
• Systematic errors mainly reduce accuracy.
• Random errors mainly reduce precision.
• Repeating measurements, calibrating equipment, and using proper measuring techniques improve the quality of experimental data.