# Quick question on accuracy (statistics)

1. Dec 5, 2006

### Elfrae

I've got nine sets of data (three people each took ten measurements of three different distances), and I need to find an estimate of the accuracy to which each person measured each distance.

I've already calculated the mean and standard deviation for each set of data, but I don't know how to estimate the accuracy. Someone mentioned using the root mean square but I'm not sure if this is correct. How do I go about this?

2. Dec 5, 2006

### courtrigrad

Look at the standard deviations of the means.

$$\sigma_{\mu_{x}} = \frac{\sigma_{x}}{\sqrt{N}}$$

Last edited: Dec 5, 2006
3. Dec 5, 2006

### Elfrae

I'm not sure I understand you. Are you saying that the standard deviation of the mean is the standard deviation of the data divided by root N? Is that the accuracy? I don't know what is meant by 'accuracy' in this context.

4. Dec 6, 2006

### HallsofIvy

Staff Emeritus
"Root mean square" is the standard deviation!

I think Courtigrad was under the impression that you wanted an "overall" accuracy for all three people, not three different accuracies.

Just as there are several different "averages" (mean, median, mode, midrange) so there are several different measures of accuracy or "dispersion".

The standard deviation is itself a perfectly good measure of "accuracy". Another is the "distance from the mean": Take the absolute value of the difference of each measurement and the mean. The "accuracy" is the largest of those: you are saying that the "true value" is the mean plus or minus that "accuracy".

5. Dec 6, 2006

### Elfrae

So there is no one definition for 'accuracy' but using the standard deviation as a value for accuracy is acceptable?

Right, now I know what the question is asking! Thank you.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook