Question

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?

Short answer

Example of four sets of measurements: a. Imprecise and inaccurate data: 9.5, 8.4, 11.1, 9.8 cm b. Precise but inaccurate data: 10.0, 10.1, 9.99, 10.05 cm c. Precise and accurate data: 10.62, 10.61, 10.63, 10.60 cm Data can be imprecise or inaccurate due to random or systematic errors caused by factors such as fluctuations in measuring instruments, environmental factors, human errors, calibration errors, and inaccurate zero-point adjustments. It is contradictory to say a set of measurements is imprecise but accurate because if the measurements are imprecise, they would not consistently indicate an accurate result, and it is impossible for imprecise data to be accurate.

Step-by-step solution

Set of measurements

For imprecise and inaccurate data, the measurements should be neither close to the true value nor to each other. An example of such measurements is: 9.5, 8.4, 11.1, 9.8 cm. #b. Precise but inaccurate data:

Set of measurements

For precise but inaccurate data, the measurements should be close to each other, but not close to the true value. An example of such measurements is: 10.0, 10.1, 9.99, 10.05 cm. #c. Precise and accurate data:

Set of measurements

For precise and accurate data, the measurements should be both close to the true value and to each other. An example of such measurements is: 10.62, 10.61, 10.63, 10.60 cm.

Explanation for imprecise or inaccurate data

A possible explanation why data can be imprecise or inaccurate is due to random or systematic errors. Random errors can be caused by various factors such as fluctuations in measuring instruments, environmental factors, or human errors. Systematic errors can be caused by calibration errors, and inaccurate zero-point adjustments among other factors.

Issue with imprecise but accurate data

It is contradictory to say a set of measurements is imprecise but accurate because in order for a set of measurements to be considered accurate, they must be close to the true value. If the measurements are imprecise, it means that they are not close to each other and would not consistently indicate an accurate result; thus, it is impossible for imprecise data to be accurate.