# Video: Measurement Accuracy and Precision

Which of the following statements most correctly describes how zero measurement errors affect the accuracy and the precision of measurements? [A] Zero errors decrease both the accuracy and the precision of measurements. [B] Zero errors decrease measurement precision. [C] Zero errors do no affect measurement accuracy or measurement precision. [D] Zero errors decrease measurement accuracy.

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### Video Transcript

Which of the following statements most correctly describes how zero measurement errors affect the accuracy and the precision of measurements? A) Zero errors decrease both the accuracy and the precision of measurements. B) Zero errors decrease measurement precision. C) Zero errors do no affect measurement accuracy or measurement precision. D) zero errors decrease measurement accuracy.

Okay, so to answer this question, we should first recall what the difference between accuracy and precision is. Simply put, the accuracy of a measurement is how close a measured value is to its true value. In other words, a measurement is accurate if the value that we measure is very close to the actual value of the quantity we’re trying to measure. So, for example, after many, many repeated measurements and many different experiments, we’ve gathered that the true value of the gravitational field strength on earth is probably 9.8 meters per second squared. However, if we were to do an experiment now to try and measure this gravitational field strength and we got a value of 25 meters per second squared, then we would say that this measurement is not very accurate because it’s not close to the true value. So that’s accuracy.

Precision, on the other hand, is a measure of whether repeated measurements under the same conditions will give the same measured values. In other words, if we were to look at our gravity measuring experiment again, where we were trying to find the gravitational field strength on Earth. And the first experiment we did, we found the value of 9.7 meters per second squared. And then, we repeated our experiment under exactly the same conditions. So basically, we did everything exactly the same way again. But this time, we got a value of 20 meters per second squared. And then, we did the experiment again, doing everything exactly the same way as before. And then, we got a value of five meters per second squared.

In this case, we would say that our experiment is not precise because every time we repeat this experiment under the same conditions, it’s giving us wildly different values. Now, this might be for various reasons. We might be making a mistake in terms of the experimental setup or the equipment that we’re using might be dodgy for example. But the idea is that precision is a measure of how close repeated measurements are to each other.

So now that we’ve looked at accuracy and precision, we need to try and work out how zero measurement errors can affect accuracy and precision. But first of all, what even is a zero measurement error? Well, a zero measurement error is simply a fault in our equipment that we’re using such that when the equipment should read zero, it reads something else instead. For example, if we have a set of weighing scales. So let’s say here is a set of weighing scales. And when there’s nothing placed on the weighing scales, that it reads zero kilograms.

Now, in this case, there is no zero measurement error for this weighing scale because it is correctly reading zero kilograms when it should read zero kilograms. There’s nothing placed on the weighing scale. However, there would be a zero measurement error if there was still nothing placed on the weighing scales. But the reading itself was not zero. Let’s say the reading was two kilograms. Well, in this case, everything that we placed on the weighing scale, we will now think it’s two kilograms heavier than it actually is. So, for example, let’s say that a person who actually weighs 70 kilograms, steps onto the scales. In this case, due to the zero measurement error, the scales will tell the person that they weigh 72 kilograms. And hence, the zero measurement error is affecting the accuracy of the measurement because the measurement on the scales 72 kilograms is not close to the true value of the person’s mass, which is 70 kilograms.

And so because of this, we can see that zero measurement errors can affect the accuracy of measurements. However, zero measurement errors will not affect the precision of measurements. And this is because the person could step off the scales and then step back on the scales again. In other words, they’ll be repeating their experiment where the experiment consists of them weighing themselves. And they would be doing this under exactly the same conditions as before. And the reading on the scales would once again be 72 kilograms when they step back on the scales. So with repeated measurements, all of the values that would be measured would be very close to each other. In other words, every time the person steps on the scales, they would measure close to 72 kilograms. And so, the precision of the experiment has not been affected. But as we’ve seen already, the accuracy has.

And hence, out of options A to D, we can rule out option A because this one says that zero errors decrease both the accuracy and the precision which we’ve seen is not true. Option B can be ruled out too because it says that zero errors decrease measurement precision, which is also not true. And we can rule out Option C, which says that zero errors do not affect measurement accuracy or measurement precision. The answer that we’re looking for is option D: zero errors decrease measurement accuracy.