Scientific Measurements: Accuracy, Precision & Percentage Error

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Accuracy, precision, and percentage error all characterize scientific measurements and tell you something about how good the measurements are. In this lesson, learn what these terms mean and how to calculate percentage error.

Making Scientific Measurements

Imagine that you are a scientist about to perform a very important experiment. You set up everything carefully, make your measurements, and find that your results are a little different from what you expected. Do you just accept these results and assume that they are correct? You shouldn't! Any time you perform scientific measurements, they should be repeated many times. Every time you make a measurement, it may be a little different from the others, but by making many measurements, you will get a better idea of the true value of the quantity you are trying to measure.

Accuracy and Precision

When you make repeated scientific measurements, it is important to know how accurate and precise they actually are. Often, you may hear the words accuracy and precision used interchangeably, but in science, they are not the same.

  • Accuracy is a measure of how close your measurements of a quantity are to the true or accepted value of the quantity.
  • Precision measures how closely repeated measurements agree with each other.

Ideally, you will always be both accurate and precise, but sometimes, a set of measurements may be accurate but not precise or precise but not accurate.

To really understand this, let's imagine that you are throwing darts at a board. If the darts were spread apart from one another, but fell all around the bullseye, the pattern would be accurate but not precise. (See the left side of the figure below.) On the other hand, if all of the darts hit near the same spot, but that spot is not the bullseye, then the pattern would be precise but not accurate. (See the right side of the figure below.) Of course, if all your darts hit exactly on the bullseye, then your dart throwing would be both accurate and precise.

accuracy and precision

What are some reasons why your measurements might be accurate but not precise? Sometimes, there is an element of randomness in what you are measuring. For example, suppose that you want to measure the temperature in a room. If you collect data in several locations, you may get slightly different values since the temperature may not be completely constant throughout the space. This would mean that, although your data would be accurate, it would not be very precise.

And what are the reasons you might be precise but not accurate? If you are not making the measurements correctly or if there is something wrong with your equipment, you could be highly precise without being accurate. For example, if you used a ruler that was chipped on the end to measure the length of a pencil, you would get the same value every time (high precision) but still wouldn't be accurate because your ruler was not showing the true value you hoped the measure.

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