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Accuracy and precision

  • Science
  • Grades 4-5
  • 321 words
  • Also written for younger readers
Accuracy: how close results are to the true value Precision: the repeatability of measurements
Accuracy: how close results are to the true value Precision: the repeatability of measurements Pekaje at English Wikipedia · gfdl · source

The accuracy and precision of measurements have special meanings in the fields of science, engineering, industry and statistics.

  • The accuracy of a measurement system is how close it gets to a quantity’s actual (true) value. JCGM 200:2008 International vocabulary of metrology — Basic and general concepts and associated terms (VIM)

  • The precision of a measurement system is the degree to which repeated measurements give the same results.

A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a error in the way it is done, then increasing the sample size generally increases precision but does not improve accuracy. The end result would be a consistent, yet inaccurate, set of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision.

A measurement system is valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).

The terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data.

In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement.

Different meanings of ‘precision’

The word “precision” also refers to how fine the measurement is made, as the resolution of the measurement, such as to the nearest meter, centimeter, or yard, foot, inch, or nanometer.

In the case of full reproducibility, such as when rounding a number to a representable floating point number, the word precision has a meaning not related to reproducibility. For example, in the IEEE 754-2008 standard, it means the number of bits in the significand (number of digits in the amount), so it is used as a measure for the relative accuracy with which a number can be shown.

Written for younger readers

Accuracy and precision, in simpler words

This version comes from Wikijunior, a set of books written for children aged 8 to 11. It is shorter and uses plainer language than the article above.

From Wikijunior: The Book of Estimation

What is precision? What is accuracy? How do we determine the precision and accuracy of something? Read this chapter to find out!

Consider the number 987,654,321.000000001. Let’s round it off to a neater number. Say, for example, to the nearest hundred. That’s 987,654,300. How accurate is that?

Excluding the last two zeros, there are seven digits. That means the number was rounded to seven significant figures (sig. figs.). A significant figure is a figure that is accurate and important in an estimated number. In the example, we know that the actual last two digits are 2 and 1, so we can be sure that the figure was rounded up to seven sig. figs.

However, sometimes we are asked to find out the number of significant figures without the actual value. If this is the case, we do not know whether the zeros are exact or not. So, we can only write ‘7, 8 or 9’.

Let’s round it off to the nearest hundredth instead. That’s 987,654,321.00. This time, there seems to be nine significant figures. Or are there? Let’s take a closer look. The last two zeros are exact. That’s because the tens and hundreds places are 0 at first. This still holds true when we are asked to name the number of sig. figs. without the exact value, because we assume that unnecessary zeros are always removed.

Here are a couple more examples to illustrate this:

Note that the three zeros after the decimal point of c) are not significant figures.

Sometimes we are asked to round up, down or off a number to a number of sig. figs. This is done the same way as rounding to a certain number of place or a certain digit.

Notice that the last number is already in three significant figures. There is no need to change it.

Accuracy is how close an estimate is to the true value. Precision is the number of significant figures you give in your estimate. These are two different things. Suppose the true population of a city is 2,432,543. If you estimate the population at 2.4 million, that is reasonably accurate. This will be accurate enough for most purposes. However, it is not very precise, being only to the nearest 100,000. If you estimate the population at 7,754,632, that is very precise. Since the number of people in a city must be a whole number, it could not be more precise. However, it is hugely inaccurate, being over three times too high.

We have just learnt how to measure precision (with significant figures). Accuracy is related to error, which we will discuss later in the book.

  • Accuracy

  • Precision

  • Significant figures

  • Most significant figure

  • Least significant figure

  • Placeholder

  • In each of the following numbers, find the number of significant figures and determine if the underlined digits are significant figures.

  • 123,456,789.10 0 0

  • 0.00000001234 0 12340

  • -23 0 .567

  • Round up, down and off the following numbers to the three significant figures.

  • 1,234,456

  • -0.00012393546

  • 345 Answers:

  • This question tests the ability to identify significant figures.

  • 123,456,789.10 0 0

  • 0.00000001234 0 12340

  • -23 0 .567

  • This question tests the ability to round numbers to a certain number of significant figures, rather than to a number of places or a certain digit.

  • Round up: 1,240,000; Round down: 1,230,000; Round off: 1,230,000

  • Round up: 0.000123; Round down: 0.000122; Round off: 0.000124

  • Round up, down and off: 345

Where this page comes from

The article above is adapted from “Accuracy and precision” on Simple English Wikipedia, by its contributors. We removed reference markers, navigation boxes and tables, expanded measurement templates into readable numbers, and kept the prose otherwise intact. The simpler version is adapted from Wikijunior on Wikibooks.

Both sources are published under CC BY-SA 4.0, so this page is published under the same licence. You may share and adapt it, including commercially, as long as you credit the original and keep the same licence.

Worksheets, answer keys and printable layouts elsewhere on K5Print are our own work and are not covered by this licence.