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 cm, give an example of four sets of measurements that would illustrate the following.

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 cm, give an example of four sets of measurements that would illustrate the following.

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November 25, 2021
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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 cm, give an example of four sets of measurements that would illustrate the following.

a. imprecise and inaccurate 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?

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 cm, give an example of four sets of measurements that would illustrate the following.

b. precise but inaccurate 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?

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 cm, give an example of four sets of measurements that would illustrate the following.

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?

Answer and ExplanationSolution by a verified expert

A

Answer
Precision and accuracy are often used

interchangeably. However, this is a common misconception. Precision refers to how close all the measurements are to each other while accuracy refers to how close the measurements are to the true value.

If the true value is 10,62 em and the student gathered imprecise and inaccurate data, this means that not only is the measurements' average not close in proximity to the true value, but they are not close to each other either.

B

Explanation
Inaccurate and imprecise data from true value 10.62 cm ==> 6.56 cm, 8.52 cm, 9.22 cm and 7.23 cm where the numbers are neither near the true value nor each other.

Answer
If the true value is 10.62 cm ===> Student gathered precise but inaccurate data ==> Measurement's average is not close in proximity to the true value but they are close to each other.

C

Explanation
Definitions of precision and accuracy in simpler terms:

When the numerical values are very close to each other, then it is called as precision. When the data from all the entries or trials are close to a particular number, then it is called as precise. For example, 10.63, 10.65, 10.62. Here, all the number are close to each other.

Now, the accuracy is defined as how much the data is close to the actual number. For example, if the actual value is 10, and your results show 3, 3.6, 4.2, It is still precise since all of the numbers are close to each other, whereas, if the data shows 10.0, 9.9, and 10.1, then the data is both precise and accurate.

A possible explanation as to why the given data can be imprecise or inaccurate:

A possible explanation for imprecise data would be the human error during experiments, such as handling of the chemicals. A possible explanation for inaccurate data would be the instrumental error which can be due to the faulty equipment.

What's wrong when said that a set of measurements is imprecise but accurate:

Measurements can never be imprecise and accurate at the same time. Imprecision means that the data is not consistent. For example, the numbers such as 4.5, 8.3, 14.1. Since the collected data is so dispersed, there is no way to say that it can be accurate.

Tip: The measurements can be precise but inaccurate, but they can never be imprecise and accurate.

Answer
c. Example of precise and accurate data, when a particular considered is 10.62:

10.63, 10.65, 10.62

Detailed explanation is given below.

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