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Question Video: Describing the Relationship between Precision and Resolution Physics • 9th Grade

Which of the following statements does not correctly describe the relationship between the precision of a set of measurements and the resolution of a measuring instrument that makes the measurements? [A] The precision of measurements is affected by uncontrolled experimental variables changing the values of the quantities being measured. The resolution of a measuring instrument is not affected by changes in the values of measured quantities. [B] The precision of measurements cannot be better than the resolution of the instrument that makes them. [C] The resolution of a measuring instrument can be applied to single measurements of a value, but precision can only be applied to a set of measurements. [D] The resolution of a measuring instrument cannot be better than the precision of the measurements made by that instrument.

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Video Transcript

Which of the following statements does not correctly describe the relationship between the precision of a set of measurements and the resolution of a measuring instrument that makes the measurements? (A) The precision of measurements is affected by uncontrolled experimental variables changing the values of the quantities being measured. The resolution of a measuring instrument is not affected by changes in the values of measured quantities. (B) The precision of measurements cannot be better than the resolution of the instrument that makes them. (C) The resolution of a measuring instrument can be applied to single measurements of a value, but precision can only be applied to a set of measurements. (D) The resolution of a measuring instrument cannot be better than the precision of the measurements made by that instrument.

To answer this question, we need to understand the relation between the precision of a set of measurements and the resolution of the instrument used to make the measurements. Let’s start by thinking about these two terms: precision and resolution.

The precision of a set of measurements is a measure of how close together the measurements are. For example, say that we used a ruler to measure the length of a pencil. Let’s say that the first time we measure its length, we take two readings, and the results are 99 millimeters and 101 millimeters. Now, let’s say that we repeat the measurements and take a second set of readings. For whatever reason, this time we measure 90 millimeters and 110 millimeters. In set one, the readings are two millimeters apart from each other. In set two, the readings are 20 millimeters apart. So, in set one, the readings are closer together than in set two. And therefore, set one is the more precise set.

Now, let’s think about the term resolution. The resolution of an instrument is the smallest unit that the instrument can legitimately measure. Let’s go back to our example of a ruler. A ruler is usually marked with a scale that goes up in millimeters so that the distance from one line to the next is one millimeter. So imagine that we measure our pencil, but the end of the pencil doesn’t line up exactly with the lines on the ruler. Instead, the end of the pencil is somewhere between the 100-millimeter mark and the 101-millimeter mark on the ruler.

Looking at this, it isn’t possible to say exactly how long the pencil is, because it isn’t perfectly lined up with a mark on the ruler. All we can really say is that the pencil length is closer to 101 millimeters than it is to 100 millimeters. Because the lines of the ruler are one millimeter apart, we’re only able to measure the length of the pencil to the nearest one-millimeter increment. This is the resolution of the ruler, one millimeter.

So, we’ve seen that the precision of a set of measurements depends on how close together the values of the measurements are. Also, we’ve seen that the resolution of a measuring instrument is the smallest unit that the instrument can reliably measure. With this in mind, let’s look at our options for this question and decide which one of these statements is not true.

We’ll clear some space to make room for a shortened version of option (A). This option essentially says “Measurement precision is affected by uncontrolled variables that change the values of measured quantities. Instrument resolution is not affected by those changes.” Let’s think about the first sentence. Can the precision of measurements be affected by uncontrolled experimental variables? Well, yes. A variable is just something that changes while the experiment takes place. We typically try to stop this by attempting to control a variable, but if we can’t control all variables, then our measurements will be affected. Usually this does happen to a certain degree, so we have measurements that aren’t totally precise.

For example, let’s say we wanted to measure the length of our pencil three times. An important variable is which pencil we measure. If we measure the same pencil three times, we would expect our results to be close together and therefore pretty precise. But, let’s say we forgot to control this variable, and we measured the lengths of three completely different pencils. The values we measured would be very different from each other and therefore much less precise.

So, uncontrolled experimental variables can affect the precision of our measurements. But can they affect the resolution of our instrument? Well, no. Concerning resolution, it doesn’t matter which pencil we measure because the markings on the ruler won’t be affected by what’s being measured. The ruler is still the same, so the resolution doesn’t change. This means that option (A) correctly describes precision and resolution. To answer this question, we’re looking for a statement that isn’t correct. So, (A) can’t be the answer.

Let’s move on to option (B): the precision of measurements cannot be better than the resolution of the instrument that makes them. Again, imagine we’re measuring the length of our pencil using a ruler. When this is the case, the smallest possible difference between two values is one millimeter. For example, we could measure the length of the pencil twice and get two values: 100 millimeters and 101 millimeters. To find the precision of these measurements, we simply find the difference between them, one millimeter. One millimeter is also equal to the resolution of the ruler.

We cannot accurately measure two different values more precisely than this, because the accuracy of the measurements is limited by the resolution of the ruler. The precision of measurements cannot be better than the resolution of the instrument we use to measure. So, statement (B) is true; it isn’t the answer we’re looking for.

Next, let’s think about (C): the resolution of a measuring instrument can be applied to single measurements of a value, but precision can only be applied to a set of measurements. It’s true that the resolution of a measuring instrument can be applied to a single measurement. In fact, every time we make a measurement, we have to bear in mind the resolution of our instrument. It is also true that precision can only be applied to a set of measurements.

Remember that precision tells us how close together the values in a set of measurements are. If we only have a single value, it doesn’t make any sense to say it’s close to itself. So, precision can only be applied to a set of two or more measurements. So, option (C) is also true, and we should eliminate it.

Finally, let’s look at (D): the resolution of a measuring instrument cannot be better than the precision of the measurements made by that instrument. Actually, it’s perfectly possible and very common for the resolution of the measuring instruments to be better than the precision of the measurements made. For example, we could measure the length of the pencil twice and get the values of 99 millimeters and 101 millimeters. To find the precision of these measurements, we find the difference between them, two millimeters.

But the resolution of the ruler is still one millimeter, because the markings on the ruler are still one millimeter apart. So, the resolution of a measuring instrument can be better than the precision of the measurements made by the instrument. So, option (D) is not a correct statement. This means that the answer to this question is option (D).

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