# December 28, 2005

## Accurate and Precise

I was helping my younger brother study for his chemisty final today, and part of the introductory chapter deals with precision and accuracy. According to his book, experimental measurements are accurate if they are close to a generally accepted published value for that particular experiment. The results are precise if you repeat the experiment multiple times and get similar numbers each time. The book went on to say that things don’t necessarily have to be both accurate and precise. They can be one, or the other, or neither, or both.

So, I can understand how something can be precise but not accurate (All the numbers are the same, they just aren’t equal to the generally accepted published value). But, how can something be accurate and not precise? For it to be accurate, wouldn’t all the numbers have to be close to the accepted value, meaning that all the numbers would also be similar to each other and therefore precise? Am I thinking too deeply into high school intro chemistry?

Bobo said,

December 30, 2005 at 5:57 pm

If you imagine a Gaussian centred around a certain point on the x-axis, then precision refers to how sharp the Gaussian is (i.e. how close it resembles an idealized delta-function).

Assuming that the “true” value of the experiment is on the x-axis, accuracy then refers to how far the peak of your Gaussian is from the “true” value.

Bobo said,

December 30, 2005 at 6:00 pm

Accuracy and precision refer specifically to a given experimental result, or a set of experimental results. And they are also relative to an idealized experimental result, which is both accurate and precise. Thus, you can have accuracy without precision, in the event that your results have huge error bars with a mean value that is precisely aligned with the “true” value.

atif said,

December 31, 2005 at 6:05 am

I would have thought that if you did an experiment and got an accurate result, but in your methods, you messed up somewhere. So your results were completely accurate, but you lacked precision in what you did. I.e. instead of adding 0.01M acid, you added 0.1M acid.

What? I never did that …

Besides, we always accurately fudged to get precisely what the answer should have been. 🙂

Thats real science for ya folks.