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 inherently implies some degree of precision. Accuracy refers to the closeness of a measured value to the true value, while precision refers to the closeness of two or more measured values to each other. If a measurement is accurate, it means it is close to the true value, indicating that the results must also be close to each other. Therefore, accuracy implies precision in the results.

Step-by-step solution

Define Accuracy

Accuracy refers to the closeness of a measured value to the true value or an accepted reference value. An accurate measurement has a little systematic error, which means it's reliable and trustworthy.

Define Precision

Precision refers to the closeness of two or more measured values to each other. It's a measure of the reproducibility of the measurement. A precise measurement has a small random error, meaning that the results are consistent even if they are not necessarily close to the true value.

Explain Why It's Incorrect to Say the Results Were Accurate but Not Precise

Saying that a measurement was accurate but not precise contradicts the definitions of accuracy and precision. An accurate measurement must be close to the true value, indicating that it has a small systematic error. On the other hand, a precise measurement must show consistency, meaning that the results are close to each other even if they are not close to the true value. If a measurement is accurate, it means it is close to the true value, which inherently implies some degree of precision. The results must be close to each other, as well as close to the true value, to be considered accurate. Therefore, it is incorrect to say that a measurement was accurate but not precise since accuracy implies precision in the results.