The diagram shows a target board and four sets of hits on it: A, B, C, and D. The shots were all aimed at the bull’s-eye of the target. Which set of hits is both accurate and precise? Which set of hits is neither accurate nor precise? Which set of hits is accurate but not precise? Which set of hits is precise but not accurate?
Okay, so clearly from the number of times that the words accurate and precise have been mentioned in this question, we’re being asked to clarify our understanding about the difference between scientific accuracy and precision. So first of all, what do scientific accuracy and precision even mean?
Well, in everyday speech, we often use accuracy and precision to mean the same thing. But in scientific terminology, they’re not the same thing. Accuracy refers to how close our experimental results are to the “true value”. And if we don’t know what the true value is, then how close they are to the accepted value, where the accepted value is the value accepted by a group of scientists after doing years and years of research and experiment to determine this value and then reaching a consensus about it.
Now generally in most cases, we don’t actually know what the true value of anything is. We only know the accepted value. For example, the value of 𝑔, the gravitational field strength of Earth, the accepted value of the gravitational field strength is 9.8 dot dot dot meters per second squared. And this is the value that we found after doing multiple years of research and experiment to try and determine the gravitational field strength of the Earth.
But in reality, we will never know the true value of 𝑔 actually is. We will only know the value that our experiments give us. And of course these experiments are always prone to error, so we might not ever find out the exact true value. However, scientific accuracy then relies on this value. An accurate scientific experiment gives results that are close to this accepted value.
Now if you’re discovering something new and there is no accepted value yet, then scientific accuracy becomes hard to determine, because of course we don’t inherently know the true value of something that you’re trying to find out. So it takes lots and lots of research before you can compare your research to that done by other scientists and see if the values that you’ve found are close to the values that they’ve found whilst also considering all the errors that we have accounted for and haven’t accounted for in our experiment.
But anyway that’s a bit too complicated. Basically accuracy is just how close your results are to the true value. Precision, however, is slightly different. Precision refers to how reproducible our measurements are when we repeat the experiment under the same conditions. In other words, an experiment is precise if the result of that experiment is similar to what we got when we previously did the same experiment under the same conditions.
In other words, we conduct an experiment and we write down its results. Then we repeat this experiment multiple times and gather even more results, once again for the same experiment. If the results that we gather are roughly similar to each other, then the experiment is said to be a precise one. If these values fluctuate a lot relative to each other, then it’s not so precise.
So in this question, we’ve been asked to find out which set of hits are accurate or precise or neither or both. Now whoever is aiming at the target was aiming at the bull’s-eye. That’s the very center of the target, the yellow bit. So which set of hits is first both accurate and precise? Well, an accurate set of hits would be very close to the yellow zone. And a precise set of hits is one where all the hits are clumped up close to each other.
So we’re looking for the set of hits that are close to the yellow zone and close to each other as well. That looks to be set A, because look, they’re close to the yellow zone, they’re very close to the bull’s-eye, and also they’re also very closely clumped up. Hence, they’re accurate and precise. So the hits in set A are both accurate and precise. Now which set of hits is neither accurate nor precise?
Well if they’re not gonna be accurate, then they have to be not close to the yellow zone. And if they’re not precise, then they have to be not clumped up together. So we’re looking at set D. Look, they’re all far away from the yellow zone or from the bull’s-eye. And they’re not precise. They’re not clumped up together either. Hence, set D is neither accurate nor precise.
Thirdly, we wanna find out which set of hits is accurate, but not precise. In this case, we’re looking for the set of hits that’s close to the bull’s eye, but the individual hits are not close to each other. And that is set C. Look, they’re all surrounding the yellow zone. They’re all relatively close to the yellow zone. But they’re not clumped up together.
The other thing is if we were to calculate where the average dart would go based on the three hits that we’ve seen in group C, then the average hit would be roughly around here somewhere. And that average is very much in the yellow zone. It’s in the bull’s-eye. Hence, this set of hits is accurate. But like we said earlier, they’re not all clumped up together. So it’s not precise. And so set C is the answer to the third part of our question.
Finally, only set B is left. So let’s see if this set is precise, but not accurate. Well, all of these hits are fairly closely clumped up together. Look, they’re all close to each other. So whoever’s been aiming at this target is very consistent. Or, to your scientific terminology, they are precise. However, look how far away these hits are from the bull’s-eye, really far. Hence, even though these hits are precise, they’re not accurate. And, as we expected, therefore the set of hits that is precise but not accurate is set B.