Accuracy and Precision

Transcript

0:00Introduction

Hello everyone! Okay, one small question before we start. The true length of a rod is three point six seven eight centimetres. Instrument A reads three point five centimetres. Instrument B reads three point three eight, with one more decimal place. So which one is better? Most students say B, more decimals, so more correct, right? Hmm, are you sure? Today we will see that better can mean two very different things: accuracy and precision. And look, JEE loves to mix up these two words to catch you. So, let's begin.

0:38Two different words: accuracy and precision

So, the first word: accuracy. Accuracy is how close your measured value is to the true value, okay? Look at the targets on screen. The orange spot in the middle is the true value, and each green dot is one reading, like a dart. Accurate means you land close to the centre. Clear? Now, in daily life, accurate and precise sound like the same word, right? But in physics, they are not. So tell me, apart from being close to the truth, what else can a better measurement mean? Yes, how finely you measure it! That is precision. Precision is how finely a quantity is measured. An instrument that reads to the nearest hundredth of a centimetre measures more finely than one that reads only to the nearest tenth, okay? In other words, precision is the resolution of the instrument: how fine a step it can show you. And there is a second way to see precision. Measure the same thing again and again. If the repeated readings are close to one another, the measurement is precise. On the target, precise means the darts are bunched together, wherever they land.

1:48Four targets, four combinations

Now, look at all four targets, from left to right. First target: the darts are bunched together, right at the centre. Close to the truth, and close to each other. So, accurate and precise. Now the second target. The darts are bunched very tightly, but up in one corner, far from the centre. What do we call this? Yes, precise, but not accurate! The readings agree with each other beautifully, so they are precise. But they all miss the centre in the same way, so they are not accurate. Remember this target; it will come back. Third target: the darts are spread all around the centre. They are not close to each other, so not precise. But on average they sit around the centre, so accurate. Interesting, right? And the last one: spread out, and away from the centre too. Neither accurate, nor precise. This is the worst case of all.

2:45JEE trap: finer scale, more accurate?

Now, a very common JEE trap, okay? Suppose you buy a costly instrument, with very fine divisions on its scale. Finer scale, so its readings are always more accurate, right? No, no, careful! See, a precise instrument is not automatically accurate. Precision only tells you how finely it measures. It does not promise that it measures correctly. Take a finely divided scale that has a zero error, a fault in the instrument itself. The arrow on screen means, this leads to: every reading is fine and precise, but every reading is wrong. That is exactly our second target: bunched, but off-centre. So what spoils accuracy? Systematic errors, which push every reading in the same direction, like that zero error. Repeat the reading again and again, and it stays wrong. And what spoils precision? Random errors, which change irregularly from reading to reading, and a coarse least count, that is, a scale with big divisions. Got it?

3:52Topper's trick: two questions, answered separately

Now a trick that toppers use. Whenever a question says accurate or precise, ask two separate questions. Question one, for accuracy: how far is the reading from the true value? Smaller gap, more accurate. Question two, for precision: how fine is the resolution of the instrument? Finer resolution, more precise. And if you get many repeated readings, check how tightly they are bunched. Answer the two questions separately, and never let one answer decide the other. Clear?

4:26Example 1: which instrument is more accurate, more precise

Now, remember our puzzle from the start? Let's finish it. The true length of a rod is three point six seven eight centimetres. Instrument A, with resolution zero point one centimetre, reads three point five centimetres. Instrument B, with resolution zero point zero one centimetre, reads three point three eight centimetres. Which is more accurate, and which is more precise? Pause the video, and try it first. Done? Okay, let's check. Accuracy first, our question one: how far is each reading from the true value? For instrument A, three point six seven eight minus three point five: zero point one seven eight centimetres. For instrument B, three point six seven eight minus three point three eight: zero point two nine eight centimetres. Oh, B is further away! Zero point one seven eight is less than zero point two nine eight. So instrument A is closer to the truth, and it is the more accurate one. See, more decimals did not mean more correct! Now question two, for precision: which instrument measures more finely? Yes, instrument B! Instrument B has a resolution of zero point zero one centimetre, which is finer than instrument A's zero point one centimetre. So instrument B is more precise. One wins accuracy, the other wins precision. That is the full answer to our puzzle. With me?

6:01Example 2: three students' readings of g compared

Now a slightly harder one. The true value of g in a laboratory is nine point eight zero metres per second squared. Three students take four readings each. Student P gets nine point eight one, nine point seven nine, nine point eight zero, and nine point eight two. Student Q gets nine point six two, nine point six one, nine point six three, and nine point six two. And student R gets nine point five, ten point one, nine point eight, and nine point nine. Describe each set. Hint: think of the four targets. Pause and try. Done? Okay, let's check. Student P: the readings are close together, and all close to nine point eight zero. So student P is accurate and precise: our first target, bunched at the centre. Absolutely perfect. Now, student Q's readings agree beautifully, from nine point six one to nine point six three. So consistent, so Q must be correct, right? No, no, careful! Compare them with the true value. They all sit near nine point six two, about zero point one eight below nine point eight zero. So student Q is precise, but not accurate. Every reading is low by about the same amount, and that is the sign of a systematic error. Our second target: bunched, but off-centre. And student R's readings jump around, from nine point five to ten point one. So R is simply wrong, isn't it? Hmm, wait. Don't judge too fast. Find the mean first. Add the four readings: thirty nine point three. Divide by four: nine point eight two five, about nine point eight three. That is what the wavy equals sign means. Very close to the true value, nine point eight zero! But the readings themselves are widely spread. So student R is accurate on average, but not precise. That is our third target. See, our three students are three of the four targets. Exactly the same story.

8:12Quick revision: accuracy, precision and systematic error

So, quick revision. Accuracy: how close you are to the true value. Precision: how fine the resolution, and how close the repeated readings are to each other. And precise does not mean accurate: a systematic error can shift every reading. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!