Question

Why is it incorrect to say that the results of a measurement were accurate but not precise?

Short answer

It is incorrect to say that the results of a measurement were accurate but not precise because accuracy refers to how closely a measurement matches the true or accepted value, and precision refers to the consistency of repeated measurements. To be accurate, a measurement must match the true value closely, which means that repeated measurements would have to be consistent and precise. Therefore, it is impossible for a measurement to be accurate without being precise.

Step-by-step solution

1. Definition of Accuracy

Accuracy is the degree to which the result of a single measurement or multiple measurements match the true value or the accepted value. If the results match the true value well, then that measurement is considered accurate. This term refers to the close measurement compared to the standard or real value.

2. Definition of Precision

Precision refers to how close the results of multiple replicated measurements are to one another. The more repeatable and consistent the measurements, the higher the precision. This term refers to the consistency and repeatability of the measuring system.

3. Relationship between Accuracy and Precision

It is crucial to understand the relationship between accuracy and precision to address the problem. For measurements to be accurate, they must be close to the true value. For measurements to be precise, they must give consistent results when repeated. It is possible to have measurements that are both accurate and precise, but it is impossible to say that a measurement is accurate and not precise.

4. Explanation of Incorrect Statement

If the result of a measurement were accurate, this would mean that the result closely matched the true or accepted value. However, to determine precision, we need to look at repeated measurements. If the repeated measurements are inconsistent and vary significantly, this would mean that the measurement is not precise. So, it is incorrect to say that the results of a measurement were accurate but not precise because to be accurate implies that the measurement result closely matched the true or accepted value - and if that were the case, repeated measurements must be consistent and therefore precise.