So, before we get into this, we have to understand the following terms and terminology. These terms sometimes get mixed up, and engineers apply the wrong term to the wrong situation in an analysis of a sensing system. So, we're going to rigidly define these following terms. And one of them is resolution, one of them is precision, one of them is accuracy, one of them is tolerance. So, resolution. Resolution is the fineness of an instrument or a sensor that can be read. I came across this gentleman's website and I really liked what I saw there. This is his explanation for resolution. Here we have an analog stopwatch that can be read to one-10th of a second, I don't know if you've ever seen these in use, but years ago when I was in high school gym, we had to run around the track and the gym teacher was out there with a stopwatch that look very much like this, timing us, how quick it took us, or how long it took us to get around the track so many times. So, this analog stopwatch can be read to a 10th of a second. Digital stopwatch can be read to 100th of a second, this particular one here. So, precision. Takes humans about a 10th of a second to respond to stimulus. So, that gym coach that's out there whether he has the analog stopwatch or he's got the digital stopwatch, takes him about a 10th of a second to respond when he sees you cross the finish line. So, this means that, a digital stopwatch, even though it has one-100th of a second resolution, it only has one-10th of a second precision. Might say, "What! How can that be?" Well that's because of this lack, this imprecision that we have in this response, this human response time. So, the definition of precision, is how repeatable a measurement is. So, precision is repeatable. Though, because of the human factor involved in this with these two stopwatches, the digital stopwatch is only repeatable to a 10th of a second. If you did a bunch of testing, over and over and over and accumulated a bunch of data, you would find that the digit in the one-100ths place is pretty close to random. It just varies all over, it doesn't tell you anything more. There's no information in that one-100th place, it's only precise to a 10th of a second. So, the 10th place, 10 to the minus one. I love this graph here. So, accuracy is correctness. How correct is the reading? How correct is the sensor reporting? How correct is the answer when we measure a sensor and turn it into a temperature in this case? How correct is it? What is its accuracy? So, this picture represents a target, imagine you're out at a gun range and you're supposed to be shooting at the target, and you have this pattern here. Okay? So, this is where we start. We improve the precision. This is improving the repeatability, as we move from this picture, to this picture, the grouping got tighter. So, it's repeatability got better. Therefore, we say it's precision is higher. The accuracy remain the same, because if we take the average of all of these and compare it to the center of the target, and we take the average of all of these and compare it to the center of the target, the average is still just as far away from the center of the target. So, we haven't done anything. We know we've improved the precision, we've improved the repeatability, the accuracy remains off. Starting from here, we improve the accuracy with the same precision, all we've done is taken this pattern and shifted it over to the center. So, it has improved accuracy with the same precision. So, relatively spread out. So think about it as a distribution. Okay. If we improve the accuracy and the precision together, then we end up with this graph. Now we've taken the repeatability, improved repeatability, and we moved it here to the accuracy or correctness. Improve the correctness. Over the years, I've had many conversations where people, talk about correctness and they really talk about accuracy, but they actually mean precision, and they say precision, and they're actually talking about accuracy and I go, "No. No. No. Hang on. We got a definitions problem here. We got to straighten that out." Tolerance, is another term you'll come across. It combines precision, that's notion of repeatability and accuracy correctness together in a single value. When we, say go to digikey, and we want to buy apart, we can buy resistors or capacitors with 10 percent tolerance or five percent tolerance. So, you can think about the mental image I have in my head for the tolerance as kind of a normal distribution graph. I'm buying a 10 K ohm resistor, and it's got of 10 percent tolerance on it. So, I think of this kind of normal, something happened to that one, that side of it there. So, if it's 10 percent of 10,000 is 1000, so it could be 500 ohms this way and 500 ohms this way. But it mostly is centered around 10,000, but there's the tolerance as it can be any individual device when you sample many, many, many, devices yields and plot their resistance, you'll see that it will form some kind of a bell-shaped curve.
