# Calculating accuracy

1. Sep 6, 2011

### elegysix

Hello, I'm doing an experiment on the speed of light, and had a simple question.
The manual says accuracy should be within 5% - does this mean the same as my percent error being within 5% ?

percent error being (V-E)/V*100% (V is accepted value, E is measured value)

thanks!

2. Sep 6, 2011

### xts

Nope. It means that if you repeat your measurement many times you should obtain results having gaussian distribution of some mean value μ and some standard deviation σ.

Absolute value of difference between your μ and true value $\left| \frac{\mu-V}{V}\right|$ is called relative systematic error, while $\sigma/V$ is a relative statistical error. I don't know to which of those errors your manual refers. If it is not clear: sum of statistical and systematic errors should be smaller than requested value.

3. Sep 6, 2011

### elegysix

I thought repeatability was known as precision, while accuracy was a measure of how close it is to the value?

4. Sep 6, 2011

### xts

Oouu... So we must to wait for explanation by some true Englishman... Maybe you are right - in my language 'accuracy' and 'precision' are exact synonyms, but maybe in English there is a nuance difference. My dictionary doesn't help

5. Sep 6, 2011

### elegysix

here's a link which describes accuracy and precision and the difference. I just want to verify if 5% accuracy means 5% error.

http://webphysics.iupui.edu/NH/Projects/TEAMS%5B2%5D/err6.htm" [Broken]

Last edited by a moderator: May 5, 2017
6. Sep 6, 2011

### allitup

The statement about the ruler measurement, it says you might expect 12.00+0.01.

Shouldn't that read 12.00 +/- 0.01?

Also, the first statement says to refer to pictures. Even the source code does not have a link. Where is the rest of the reference?

Last edited by a moderator: May 5, 2017
7. Sep 6, 2011

### 256bits

It is a distinction within physics what the 2 words mean.
If you are shooting at a bull's eye with a projectile, say a gun or arrow:

1. Accurate and precise - All shots hit the center.
2. Acurate but not precise - All shots hit the target anywhere but are distributed
around the centre
3. Not accurate but precise - All shots are distributed off from the centre and
4. Not accurate not precise - Shots show no pattern or no mathematical analysis possible.

Hope that helps.

8. Sep 6, 2011

### 256bits

It would mean that any value you obtain by your experiment should be within 5% of the accepted value.

I would take the percent error as follows:
You percent error would be calculated from the setup of the apparatus. You would maybe be measuring several lengths, frequency, etc, etc and all would have measurement errors.
XTS explains what that entails, and you want to make these errors as small as possible to reach an accuracy of 5% in your experiment. Comparing what you think you should get to what you do get as a measured outcome of the experiment lets you know if your apparatus needs adjustment.