Video: Measurement Accuracy and Precision

Which of the following statements most correctly describes the meaning of accuracy of measurements? [A] An accurate measurement has a value that is the same value when a quantity is repeatedly measured. [B] The more accurate the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity. [C] An accurate measurement is made using a correct measurement method. [D] The more accurate the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.

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Video Transcript

Which of the following statements most correctly describes the meaning of accuracy of measurements?

Okay, let’s go through these statements one by one. A) An accurate measurement has a value that is the same value when a quantity is repeatedly measured. Now to set this up a bit, let’s say that this quantity that we’re measuring has some true accurate value. We’ll call that value 𝑇. And what we’re doing is we’re making measurements of this quantity with the hope that those measurements reveal to us 𝑇, that true value. So we make a series of measurements. And their results we can call 𝑀 one, 𝑀 two, 𝑀 three, and so forth. Now this option A is saying that if 𝑀 one, 𝑀 two, 𝑀 three, and the other measured values we have all have the same value, then that’s what an accurate measurement is. But notice that all these measurements could be the same thing and yet be very different from our true value 𝑇. So just because our measured values agree with one another, just because they have the same value doesn’t mean our measurement is accurate. So option A is off our list.

Moving on to option B, the more accurate the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity. Similar to option A, option B is comparing these measured values one to another, and it’s not comparing them to the true value 𝑇. Option B is saying that the closer 𝑀 one, 𝑀 two, 𝑀 three, and so on are together, the more accurate the measurement is. But again, this leaves out a comparison with the true value of this quantity. So option B can’t be our choice either.

Option C says that an accurate measurement is made using a correct measurement method. It’s true that using a correct measurement method makes it more likely that our measurement will be accurate, but it doesn’t make it inevitable. It’s possible to have a perfectly correct measurement method. But to execute that method incorrectly, leading to measurement values which are not accurate. That is, do not match up closely with the true value of the quantity we’re measuring. So option C doesn’t seem like it will be our choice either.

On then, to our last hope, option D. This says the more accurate the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity. In Option D, for the first time, we’re talking about making a comparison between the measured quantities and the true value of the quantity we’re measuring. Option D says that the smaller that gap is, the smaller the difference between the true value and a measured value, the more accurate that measured value is. And this is true. Accuracy refers to a comparison between the true value of some quantity and the measured value of that quantity. This then is the statement that most correctly describes the meaning of accuracy of measurements.

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