Question

A textbook has a mass of 5.75kg. When determining the mass in the lab, 5 groups of students came up with measurements of 4.16kg, 4.15kg, 4.15kg, 4.14kg, and 4.16kg. Categorize this data as only accurate, only precise, both accurate and precise, or neither accurate nor precise. Explain all of your conclusions (explain why or why not for both accuracy and precision).

Answer 1

The students' measurements are only precise but not accurate, as they consistently produced similar results to each other but far from the true mass of the textbook.

Step-by-step explanation:

When evaluating the measurements obtained by the students, we need to consider both the concepts of accuracy and precision. Accuracy refers to how close a measurement is to the true or accepted value, while precision refers to the consistency of repeated measurements.

In this case, the true mass of the textbook is 5.75kg, but the measurements recorded by the students are 4.16kg, 4.15kg, 4.15kg, 4.14kg, and 4.16kg. Since none of these measurements are close to the actual mass, they are not accurate. However, the measurements are very close to each other, with minor variations, indicating that they are precise, because they show consistency.

Thus, the student's data is categorized as only precise because the measurements are consistent with each other yet far from the true value. This indicates that there might have been a systematic error in the measurement process or the scale used might have been improperly calibrated.