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Chapter 1: Problem 24

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 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

Expert verified
A. Imprecise and Inaccurate Data: {10.2, 10.8, 11.0, 10.0} B. Precise but Inaccurate Data: {10.8, 10.82, 10.78, 10.79} C. Precise and Accurate Data: {10.61, 10.62, 10.63, 10.60} Imprecision and inaccuracy can be caused by human errors, variation in the experiment, or low-quality measuring instruments. It is contradictory to claim that a set of measurements is imprecise but accurate, as accurate measurements must be close to each other (precise).

Step by step solution

01

A. Imprecise and Inaccurate Data #

An example of a set of measurements that are both imprecise and inaccurate are: {10.2, 10.8, 11.0, 10.0}. These measurements are spread far apart from each other (imprecise) and are also not close to the true value of 10.62 cm (inaccurate).
02

B. Precise but Inaccurate Data #

An example of a set of measurements that are precise but inaccurate are: {10.8, 10.82, 10.78, 10.79}. These measurements are close to each other, which indicates high precision. However, they are all not close to the true value of 10.62 cm (inaccurate).
03

C. Precise and Accurate Data #

An example of a set of measurements that are both precise and accurate are: {10.61, 10.62, 10.63, 10.60}. These measurements are close to each other (precise) and also close to the true value of 10.62 cm (accurate).
04

Reason for Imprecision and Inaccuracy #

The imprecision or inaccuracy in data can be due to multiple reasons, such as human errors, variation in the experiment, or having a low-quality measuring instrument. It is essential to identify the cause of errors and try to mitigate their effect on the experiment to improve the reliability of the measurements.
05

Problem with Imprecise and Accurate Measurements #

Saying a set of measurements is imprecise but accurate is contradictory. If a set of measurements is accurate, it means they are close to the true value, which also implies that they should be close to each other (precise). It is not possible to have measurements that are both imprecise (spread apart) and accurate (close to the true value) at the same time.

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Most popular questions from this chapter

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