Question Video: Measurement Accuracy and Precision Physics • 9th Grade

Which of the following statements most correctly describes the meaning of the precision of measurements? [A] A precise measurement is more accurate than an accurate measurement. [B] The more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity. [C] A precise measurement is made using a correct measurement method. [D] The more precise 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.

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Video Transcript

Which of the following statements most correctly describes the meaning of the precision of measurements? A) A precise measurement is more accurate than an accurate measurement. B) The more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity. C) A precise measurement is made using a correct measurement method. D) The more precise 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.

Okay, we can see that the answer to this question is all about the specific meaning of the word precision when it comes to making measurements. We have these four different candidates for the most correct description of the precision of measurements. So let’s go through them one by one and evaluate each in turn.

Option A says that a precise measurement is more accurate than an accurate measurement. Now, one thing this option gets right is that it acknowledges that there’s a difference between a precise measurement and an accurate measurement. They don’t mean the same thing. But what it doesn’t get right is in claiming that a precise measurement is more accurate than an accurate one. Because precision and accuracy are two different terms with two different meanings, a precise measurement will not be more accurate than an accurate one. We can cross off option A then.

Option B says that the more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity. So option B is saying that we have these two values: a measured one and the actual correct one for some quantity. And it says that the closer these two values are, the more precise the measurement is. But this statement is confusing the terms for precision and accuracy. If we replace this word “precise” with the word “accurate,” then this description would be correct. The closeness of a measured value to an actual true value is the meaning of an accurate measurement. But because precision and accuracy don’t mean the same thing, Option B is not a correct description of a precise measurement.

Moving on to option C, this says that a precise measurement is made using a correct measurement method. Well, it’s certainly more likely that using a correct measurement method will lead to a precise measurement. But that’s not always the case. It’s possible, for example, to have a correct measurement method. But the way we carry out that method has errors in it. And those errors, which would influence the measurements we would make, might lead to imprecise measurements. Overall then, option C is not looking like a great choice. But because it’s not explicitly incorrect, let’s table it for now, keep it in mind, and then move on to our last choice, option D.

This option says that the more precise 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. Now here’s what this description is saying. Let’s say that we have some true value for a quantity. And we’ll call that value 𝑉. This could be the length of an object or its mass. But the point is it’s the accurate representation of that quantity. In order to discover what that correct quantity is, we make a series of measurements. We can say that the result of our first measurement is 𝑀 one. And then we make another measurement 𝑀 two, another one 𝑀 three, and so on. We can make any number of these measurements attempting to figure out the true value of the quantity we’re interested in.

Now, statement D is not talking about this true value 𝑉. What it’s comparing is the different measured values of this quantity one to another. And it’s saying that the smaller the difference between these measured values, the more precise our measurement is. And this is a good description of measurement precision. It compares measured values to one another and says the closer they are to one another, the more precise our measurements are. Since option D is an explicitly correct description of the precision of measurements, we choose this as our answer.

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