math - 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.