4 Tutorials that teach Accuracy and Precision in Measurements
Take your pick:
Accuracy and Precision in Measurements

Accuracy and Precision in Measurements

Author: Jonathan Osters

This lesson will explain accuracy and precision in measurements.

See More
Introduction to Statistics

Get a load of these stats.
Our Intro to Stats course is only $329.

Sophia's online courses not only save you money, but also are eligible for credit transfer to over 2,000 colleges and universities.*
Start a free trial now.


Source: Bullseye Image, Public Domain: http://en.wikipedia.org/wiki/File:Colored_Bullseye.png

Video Transcription

Download PDF

In this tutorial, you're going to learn about accuracy in measurement versus precision. And those are two different things. When we're talking about accuracy, we're talking about how close our measurements are to what the measurement should have been. The true value, versus with precision, all we're concerned about is how consistent the measurements that we take are to each other, how close are they to a single value, regardless of whether or not it's the right answer.

So let's take a look at an example. Suppose that I worked for a consumer report company. And I took someone who wears 161.8 pounds and placed them on each of four scales, five times each. And I need to decide whether each of these scales-- 1, 2, 3, and 4-- are accurate or precise or both or neither.

And so let's look at Scale 1. Scale 1 has values of 160.4, 158.8, 161.4, 164.2 and 162. Determine if that's accurate, precise, both, or neither. Pause the video and figure that out.

What you should have come up with is that this scale is accurate. It's accurate because these average out to the right answer. But they can be fairly low, like this one, or fairly high, like that one. But by and large, they'll average out to what's pretty close to the right answer.

But because they are not close to a single value every time, we're going to say that they're not precise. Do the same thing. Pause the video and figure it out for Scale 2.

What you should have come up with for Scale 2 is that it is in fact precise. You can tell just by looking at this. All of these values are within 1 pound of each other. So it is precise. But take a look. It's overestimating by at least 7 pounds. And so we're going to say that it's not accurate.

One more time-- Scale 3. What you should see for Scale 3 is that it's both accurate and precise. All of these are within a pound of each other. And they're very close to the 161.8 that we should have gotten.

Last one-- let's look at Scale 4. Pause the video one more time. What you should have come up with for Scale 4 is that this one's actually neither precise nor accurate. It actually did get the right answer once. But if you look at the five measurements taken as a whole, they're pretty far off. And they tend to overestimate.

And so we're saying that it's not going to be accurate. Because they don't really center around the right number all that much. In fact, they don't center around the right number at all. And they're not precise. Because these values aren't even that close to each other. And so for my money, if I was part of the consumer report, I would pick Scale 3.

Let's take another look at another example. And this is a very popular example of precision and accuracy. And this is with a dartboard. Assuming that we're going for the bullseye, these darts are both accurate and precise. They're tightly clustered around a single value. And that value is the bullseye.

These darts are precise, but not accurate. They're clustered around a single point. But that point isn't the right point. It's not the bullseye. These darts are in fact clustered around the bullseye, but not very tightly. And so we'll say they're accurate. Because there's not really any pattern to how they're off. This person's just not very good at darts.

And this person-- if you look at where these are clustered, they're all pretty low. There's a systematic way to how they're off. They're clustered around the bottom half of the dartboard. So it's not accurate. And they're all over the place on the bottom half. So they're not precise, either.

So to recap, important considerations are accuracy, which is how close the measurements are to the right answer, and precision, how consistent measurements are with each other. And ideally, we would like high accuracy and high precision. So we compared and contrasted accuracy with precision. Good luck. And we'll see you next time.

  • Accuracy

    The extent to which the values, when considered all together, center around the correct value for a variable.

  • Precision

    The extent to which the values are very close to each other, even if they are not near the correct value.