What is the difference between 'precision' and 'accuracy'? [closed]

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!

Contrarily

Start with the obvious reference: en.wikipedia.org/wiki/Precision_vs._accuracy – Horseshoe

physicskey.com/143/… – Senter

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.

Iman

Wolfram Mathworld states that 'the accuracy of a number is given by the number of significant digits to the right of the decimal point.' – Hypogenous

@Mike, as hesitant as I am to argue math with Wolfram, I'm not sure I agree with that. When you're thinking about the number 1234, then 1230 and 1200 differ in accuracy even though they have the same number of significant places after the decimal point. I think a better indication is just the number of significant digits (1230 has three, 1200 has two), nothing to do with a decimal point. – Iman

I didn't agree with Wolfram either but I just thought it was something interesting and provocative to note. – Hypogenous

I've logged a comment to Wolfram to get their take on it. I guess I'll either be thanked for pointing it out, or educated as to my math abilities :-) – Iman

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.

Churr

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

Troop

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.

Pasqualepasqueflower

Actually, any good dart player would be going for the triple-20 at the start rather than the bullseye but your point is valid :-) – Iman

Answer 5

Accuracy are very often confused with precision but they are much different.

Accuracy is degree to which the measured value agrees with true value. Example-Our objective is to make rod of 25mm And we are able to make it of 25 mm then it is accurate.

Precision is the repeatability of the measuring process. Example-Our objective is to make 10 rods of 25mm and we make all rods of 24mm then we are precise as we make all rods of same size,but it is not accurate as true value is 25 mm.

Gonzalez

Answer 6

Precision and accuracy are defined by significant digits. Accuracy is defined by the number of significant digits while precision is identified by the location of the last significant digit. For instance the number 1234 is more accurate than 0.123 because 1234 had more significant digits. The number 0.123 is more precise because the 3 (last significant figure) is in the thousandths place. Both types of digits typically only relevant because they are the results of a measurement. For instance, you can have a decimal number that's exact such as 0.123 such as 123/1000 as defined, thus the discussion of precision has no real meaning because 0.123 was given or defined;however, if you were to measure something and come up with that value, then 0.123 indicates the precision of the tool used to measure it.

The real confusion occurs when combining these numbers such as adding, subtracting, multiply and dividing. For example, when adding two numbers that are the result of a measurement, the answer can only be as precise as the least precise number. Think of it as a chain is only as strong as its weakest link.

Sidetrack

Answer 7

enter image description here

I think that picture is accurate. Not precisely.

Shu