What is the difference between 'precision' and 'accuracy'?

Question

What is the difference between 'accurate' and 'precise' ?

If there is a difference, can you give an example of

• a number that is accurate but not precise
• a number that is precise but not accurate
• a number that is both accurate and precise

Thanks!

Answer 1

Precision refers to how much information is conveyed by a number (in terms of number of digits) whereas accuracy is a measure of "correctness".

Let's take the π approximation ²²/₇, for our purposes, 3.142857143.

For your specific questions:

• a number that is accurate but not precise: 3.14. That's certainly accurate in terms of closeness, given the precision available. There is no other number with three significant digits that is closer to the target (both 3.13 and 3.15 are further away from the real value).

• a number that is precise but not accurate: 99999.12345678901234567890. That's much more precise since it conveys more information. Unfortunately its accuracy is way off since it's nowhere near the target value.

• a number that is both accurate and precise: 3.142857143. You can get more precise (by tacking zeros on the end) but no more accurate.

Of course, that's if the target number is actually 3.142857143. If it's ²²/₇, then you can get more accurate and precise, since 3.142857143 * 7 = 22.000000001. The actual decimal number for that fraction is an infinitely repeating one (in base 10):

3 . 142857 142857 142857 142857 142857 ...

and so on, so you can keep adding precision and accuracy in that representation by continuing to repeat that group of six digits. Or, you can maximise both by just using ²²/₇.

Answer 2

One way to think of it is this:

• A number that is "precise" has a lot of digits. But it might not be very correct.
• A number that is "accurate" is correct, but may not have a lot of digits.

Examples:

• 3.14 is an "accurate" approximation to Pi. But it is not very precise.
• 3.13198408654198 is a very "precise" approximation to Pi, but it is not accurate,
• 3.14159265358979 is both accurate and precise.

So precision gives a lot of information. But says nothing about how correct it is.

Accuracy says how correct the information is, but says nothing about how much information there is.

Answer 3

Assume the exact time right now is 13:01:03.1234

• Accurate but not precise - it's 13:00 +/- 0:05
• Precise but not accurate - it's 13:15:01.1425
• Accurate and precise - it's 13:01:03.1234

Answer 4

The standard example I always heard involved a dart board:

• accurate but not precise: lots of darts scattered evenly all over the dart board
• precise but not accurate: lots of darts concentrated in one spot of the dart board, that is not the bull's eye
• both: lots of darts concentrated in the bull's eye

Accuracy is about getting the right answer. Precision is about repeatedly getting the same answer.