Definition
Accuracy describes how close a measured value is to the true or accepted value.
Precision describes how close repeated measurements are to one another.
A measurement can be accurate, precise, both, or neither.
Accuracy
Accuracy indicates the correctness of a measurement.
The closer the measured value is to the accepted or true value, the higher its accuracy.
Accuracy is mainly affected by systematic errors, which shift measurements consistently away from the true value.
Precision
Precision indicates the consistency or repeatability of measurements.
If repeated measurements are close to one another, the measurements are said to be precise, even if they are not close to the true value.
Precision is mainly affected by random errors, which cause measurements to fluctuate unpredictably.
Relationship Between Accuracy and Precision
Accuracy and precision describe different aspects of measurement quality.
High precision does not necessarily imply high accuracy, and high accuracy does not necessarily imply high precision.
The best measurements are both accurate and precise.
Possible Situations
| Accuracy | Precision | Description |
| High | High | Measurements are close to the true value and close to one another. |
| High | Low | Measurements are scattered but average near the true value. |
| Low | High | Measurements are consistent but systematically offset from the true value. |
| Low | Low | Measurements are scattered and not close to the true value. |
Example 1
The true length of an object is 50.0 cm.
Student A measures:
49.9 cm, 50.0 cm, 50.1 cm, 50.0 cm
These measurements are both accurate and precise.
Example 2
The true length is still 50.0 cm.
Student B measures:
52.1 cm, 52.0 cm, 52.1 cm, 52.0 cm
These measurements are precise because they are highly consistent, but not accurate because they are far from the true value.
Example 3
Student C measures:
48.6 cm, 50.8 cm, 49.5 cm, 51.2 cm
The measurements are widely scattered but their average is close to 50.0 cm.
These measurements are accurate on average but not precise.
Example 4
Student D measures:
47.8 cm, 52.4 cm, 49.1 cm, 53.0 cm
The measurements are neither close to one another nor close to the true value.
They are neither accurate nor precise.
Key Points
- Accuracy describes closeness to the true value.
- Precision describes the consistency of repeated measurements.
- Systematic errors mainly reduce accuracy.
- Random errors mainly reduce precision.
- Good measurements are both accurate and precise.