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About this Lesson
 Type: Video Tutorial
 Length: 15:37
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 167 MB
 Posted: 01/28/2009
This lesson is part of the following series:
Chemistry: Full Course (303 lessons, $198.00)
Chemistry Review (25 lessons, $49.50)
Chemistry: Introduction to Matter and Measurement (13 lessons, $14.85)
Chemistry: Scientific Measurement (5 lessons, $7.92)
In this lesson, Prof. Yee discusses precision and accuracy in measurements. He explains that all measurements will have a degree of uncertainty due to instrumentation, and the range of uncertainty will appear in the last digit of the measurement. You want to have measurements that are both precise and accurate. Precision is the reproducibility of the measurement of a quantity and is tied to the concept of random error. Prof. Yee uses a ruler as an example of precision. Accuracy refers to how close a measurement is to a hypothetical true value. It is possible for a measurement to be precise but not accurate if there is a systematic error. Systematic error is an error inherent to the measurement of a value, such as a clock that is consistently 5 minutes fast. Finally, Prof. Yee explains the relationship between precision and accuracy using a game of darts.
Taught by Professor Yee, this lesson was selected from a broader, comprehensive course, Chemistry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidationreduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more."
Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies moleculebased magnetism.
About this Author
 Thinkwell
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More..Recent Reviews
 it all makes sense now
 07/01/2010

I am attending an online university and all of the resources explaining these concepts were written. I am a visual learner, especially when it comes to abstract concepts so I really wasn't getting a grasp on this subject. I am studying to be a biology teacher and one of my assignments was to create a lesson teaching students about accuracy and precision, but I didn't really understand it myself. I have seen many examples with the dart board, but I was not making the connection between that and significant figures. the teacher in this video made it so simple t understand, using practical examples and i got it right away. this video totally saved me (and the otherwise unfortunate students that would have gotten a subpar lesson)!
An Introduction to Matter and Measurement
Scientific Measurement
Precision and Accuracy Page [1 of 3]
This may not be an obvious concept, but whenever we make a measurement – first of all, we have to have units
associated with that measurement – but what may not be obvious is that there is uncertainty associated with that
measurement. And the idea is that if I step on a bathroom scale and it says that I weight 166 pounds, I don’t weigh
necessarily exactly 166 pounds. I might weigh 166.1, 166.2, 165.7, and the scale is still going to report 166 pounds.
So, in other words, there is uncertainty in that measurement, and the uncertainty is actually in the last digit. So, in
other words, 166 really means only that we can say that I’m more than 165 and less than 167. So, conventionally,
what people say is that if they write 166, what’s implied is that it’s plus or minus 1 in the last digit. In other words, if it’s
minus 165 and if it’s plus 167. And we call this the uncertainty and the uncertainty appears in the last digit. We know
that it’s not 170. That would be uncertainty in this digit. We know it’s not as high as 170, but we can’t be sure that it
isn’t as small as maybe a hair above 165, or just a little bit below 167.
Now, that notion of uncertainty is important when we’re making measurements in chemistry or in science in general,
because what we report is we report a number and it has an implied uncertainty associated with it. So I can pose the
question, “Is there a difference between 166 pounds and 166.0 pounds?” And to you, as a person just stepping on
the scale, maybe not. But to a scientist, there is definitely a difference, because 166 implied uncertainty of plus or
minus 1 means that the value that we measured can be between 165 and 167. We know it’s bracketed by those two
numbers, but we can’t be precisely sure about what the real value of the number is, whereas 166.0 has a different
implied precision. The precision is in the last digit, and the last digit can vary by plus or minus one in this digit. So, in
other words, the number is between 165.9, which is this number minus .1, or this number plus 1. So, in other words,
we’ve narrowed the region or the range over which the measurements are going to appear. So if we repeat the
measurement more than once on the bathroom scale, we’ll always get numbers between 165 and 167, whereas if we
have this super colossal, really expensive bathroom scale that measures to tenths of a pound instead of just to the
nearest pound, then our measurements are going to appear in a narrower range and what we say is that reporting it
as 166.0 is more precise than reporting it just as 166.
One thing I forgot to mention is that the symbol for pounds is lb., so you’re going to see lb.’s after all my
measurements. Remember, measurements always have units associated with them. But if this looks like 16, I
apologize for my handwriting. Remember, it’s lb. for pounds. I have no idea why lb. is the unit for pounds.
Now, precision is tied to the concept of random error. And, unfortunately, random error is a pour choice, but that’s just
what it’s called. It isn’t random in the sense of rolling dice, what it’s random is that, in the last digit, you have to
sometimes, in fact, you always, have to guesstimate, guessestimate. And that idea is what is known as random error.
So when we say that something has high precision, what we mean is that we can make the measurement over and
over again and the values fall within a narrow range, taking into account the fact that you have to guesstimate the last
digit. And let’s see what I mean by that.
So precision, again, reflects the uncertainty in the last digit. If we can know that last digit, then we can say that the
number is more precise. And rather than belabor that point, let me just show you my illustration. Suppose we want to
measure this pink bar here, and I have a blowup of a ruler. And this ruler happens to be marked in centimeters.
Then, if we have to know, using this ruler, how long this pink bar is, the best we can do is – well, we know it’s between
1 and 0. And, furthermore, we can actually guesstimate what the next digit is, because we can say qualitatively,
“Okay, well, it’s a little bit longer than ½. And it looks like it’s less than ¾. Here’s ¾, here’s ½. Let’s say that it’s about
.7.” So, in other words, beyond whatever is marked on the ruler or on the bathroom scale or whatever, you can
always guesstimate the next digit. And the next digit in this case is going to be, say, a 7. So we know it’s between 0
and 1, but we can do better than that. We can say that our pink bar is .7 centimeters. And that involves that
guesstimate that I’m talking about. And you always have to do that with the measurement, because the device that
you use, there’s always some intrinsic limit. In other words, in this case the bar is marked down to centimeters, and
so you can go one better than that and guess the next number, which is the 7, but there’s uncertainty. It’s between 6
and 8, but we don’t know for sure that it’s exactly .7.
Now, if we had a different ruler, one that was, say, marked in millimeters as well, now we can actually improve our
precision, because we can say for sure that not only is it between 0 and 1, but, in fact, it’s between .6 and .7. And
then, once again, we can guess what that next digit should be. And so, using our ruler that has more demarcations,
we can say that the number is now 0.6 and we can guess the next digit to be 5. What does this say? .7 says that the
number is 0.7 plus or minus 0.1, meaning that the number is really between .6 and .8, and now, with our better ruler,
An Introduction to Matter and Measurement
Scientific Measurement
Precision and Accuracy Page [2 of 3]
we can say that this is 0.65 plus or minus 0.01. So we’ve made a more precise measurement with this ruler than with
this ruler.
Now, the other term that you have to think about when you’re worrying about measurements is accuracy. And
accuracy is how close your measured value is to the hypothetical true value. So I weight something, and I don’t know
exactly what I weigh. The scale tells me that I weigh 166. And somewhere in a theoretical sense, there is exactly
what I really weigh and the scale just measures and tells me approximately what I weigh. Well, accuracy then is how
close you are to the real true value, and it depends on the quality of the instrument that I’m using. For instance, is it
calibrated? So understand that accuracy is not about how many marks does it have, it actually is a reflection of how
good is my instrument. For instance, imagine I’m stepping on this bathroom scale and the bathroom scale tells me
that I weigh 166. And suppose I didn’t notice that, in fact, before I stepped on the scale it was actually set up on –1.
So, in other words, it wasn’t exactly 0 when I got started. Well, that’s going to give me the wrong answer. It’s going to
give me the wrong answer, because the scale that I’m using isn’t accurate. And, in fact, it’s entirely possible for a
measurement to be precise and not even accurate at all. For instance, I could have the scale that tells me that I’m
166.0 pounds and, if I measure it again, and again, and again and measure myself over and over, I’ll keep getting
166.0 pounds. But if the scale wasn’t calibrated, in other words, if it started out at –1, I might really weigh, my true
weight is going to be 167. So I’m getting a reproducible number that I can express to a very precise value, but it’s just
wrong. And that’s an entirely possible situation, that if you have a device that gives the same answer over and over
again, but the answer isn’t tied to the true answer, then it is precise without being accurate. And I’ll give you an
example of that in a second.
Now, accuracy, in contrast, is tied to the idea of a systematic error. If you have a systematic error, what it means is
that your system is no good, that your system, being the scale, or the ruler or whatever, isn’t any good. It could give
answers in a very narrow range, so it could be very precise, but if it’s wrong, if it’s just not close to what the true value
is, then we’d say that it isn’t accurate. And a great example of that is a clock that maybe measures in milliseconds. A
millisecond is a thousandth of a second. So it gives us a very precise number of about what time it is, but suppose it’s
5 minutes fast? Well, it’s 5 minutes fast, meaning that it’s giving the wrong time all the time, but it’s giving it down to
the millisecond. Now, that could be useful still, if you know what the error is, if you know what the nature of the error
is. For instance, if your watch is always 5 minutes fast, you know what time it is. But, in general, what we’re going to
see is that numbers that are precise tend to be more accurate. So, in other words, if you can express things down to
milliseconds, if a scientist can come up with a device that measures down to milliseconds, usually it’s also going to be
accurate, meaning that it’s also going to be close to what the true value is.
And the flip side, so you might have said, “Okay, well, we can have a number that is precise, but not accurate. Can
we have something that’s accurate, but not precise?” And that’s sort of a band term. In other words, it’s not really
meaningful to say that something is accurate, but not precise, because remember, accuracy refers to how close
something is to the true value. And so if the data are scatter, so, in other words, if the values appear all over the
place, but they just average out to be close to what the true value is, that’s not really meaningful. And the best way to
understand this concept is to look at someone playing darts. So what we’re going to do is we’re going to go to the pub
and we’re going to throw some darts, and I’m going to finish this lecture there. But the bottom line is that for
something to be accurate, but not precise, is not really meaningful, whereas precise, but not accurate, is very
meaningful. And, generally, the more precise something is, the more accurate we at least hope it’s going to be.
We’re here at a local Austin watering hole to finish our discussion of precision and accuracy. And the classic analogy
for precision and accuracy is a game of darts, where the true value is given by the target and the precision indicated
by how close the darts are clustered together. So what we have here certainly is a throw that is precise, and this is
the first throw that I made today. So even before the cameras were set up, I just walked up – I haven’t played darts in
a couple of years probably – grabbed the darts, toed the line and threw these three darts. I swear. And you can see
that we have a precise measurement, the darts are close together. It might seem to you that it isn’t a very accurate
throw, if you thought that the target was the bull’s eye. But, in fact, as any true dart player knows, you shoot for the
triple 20, and that’s what my target was, so that’s what we’re going to call the true value. And you can see that my
measurement was very close to the true value. So this is both a precise and an accurate measurement. Now let me
show you what the analogy would be for a measurement that is neither precise nor accurate.
Now the way Professor Harmon throws darts is like this. And that throw is certainly not precise, because the darts are
not clustered together, but it also is accurate in the sense that, if the target were the bull’s eye, the true value lies
An Introduction to Matter and Measurement
Scientific Measurement
Precision and Accuracy Page [3 of 3]
somewhere close. But you can see that the concept of accuracy also requires precision. In other words, you can’t be
accidentally accurate. You’re certainly not going to win any tournaments with throws like this, even if the average
value is somewhere close to your target. And finally, let me show you what a throw that is precise, but not accurate.
That would be a throw where the darts are clustered together, but nowhere near the true value or the target that I’m
aiming for.
So let’s suppose that the true value is still the triple 20. And now I’m going to throw the darts, and let’s see how well I
do, aiming for a precise measurement. Okay, this is obviously not as good as what I did before, but you can see that
the darts are reasonably clustered together, so that would suggest that they are reasonably precise. Not going to win
any tournaments with this either, but not accurate, meaning not anywhere near the triple 20.
And finally, let me try again to see if I can throw and hit the triple 20, something that is both precise and accurate.
Well, 2 out of 3 isn’t bad. It’s not good either. But again, let me remind you that precision is reproducibility. It’s how
close the individual measurements cluster together with each other, and so this is not real precise. If it were like that,
that would be precise. And then accuracy refers to how close our measured value is to the true value. In this case,
the true value is the triple 20, so we’re not super close, but it’s not bad either, and that you can have a measurement
that is precise, but not accurate, such as a throw where the darts are clustered together, but nowhere near the true
value. And a throw that is accurate and precise is one where they’re clustered about the true value.
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I am attending an online university and all of the resources explaining these concepts were written. I am a visual learner, especially when it comes to abstract concepts so I really wasn't getting a grasp on this subject. I am studying to be a biology teacher and one of my assignments was to create a lesson teaching students about accuracy and precision, but I didn't really understand it myself. I have seen many examples with the dart board, but I was not making the connection between that and significant figures. the teacher in this video made it so simple t understand, using practical examples and i got it right away. this video totally saved me (and the otherwise unfortunate students that would have gotten a subpar lesson)!