To determine the volume of a cube, a student measured one of the dimensions of the cube several times. If the true dimension of the cube is \(10.62 \mathrm{~cm}\), give an example of four sets of measurements that would illustrate the following. a. imprecise and inaccurate data b. precise but inaccurate data c. precise and accurate data Give a possible explanation as to why data can be imprecise or inaccurate. What is wrong with saying a set of measurements is imprecise but accurate?

Set 1: Imprecise and Inaccurate Data - Example measurements: {10.1, 10.8, 11.6, 9.7} cm Set 2: Precise but Inaccurate Data - Example measurements: {11.2, 11.3, 11.1, 11.4} cm Set 3: Precise and Accurate Data - Example measurements: {10.6, 10.7, 10.5, 10.6} cm Possible explanations for imprecise or inaccurate data include faulty or low-quality measuring tools, human error, external factors, or natural fluctuations in the measured property. It's difficult to have a set of measurements that are imprecise but accurate, as having a higher precision means the measurements are closer to each other, and being accurate means they are close to the true value. If the data points are not close to each other (imprecise), it would be improbable to have them be close to the true value on average (accurate).