# Representation of standard deviation in statistical range

I have computed the mean and standard deviation of a variable in a dataset, and I wish to represent these values in a report. Is the following the correct way to go about this?

$1.23 \pm 0.52 \sigma$,

where the mean is 1.23 and the standard deviation is 0.52.

Alternatively, would a standard error be a more appropriate thing to report? The results are classification accuracies and the time taken to compute them.

• As long as you make it clear what you are reporting, you're OK, but the usual method of reporting means and sds, as far as I've seen, is mean = 1.23 (sd = 0.52) or something similar. The $\pm$ sign used the way you are proposing risks confusing people into thinking it is a 95% CI, which it isn't. Commented Oct 3, 2012 at 12:35

It looks like you want to make a confidence interval. If that's not what you are trying to do, and you just want to report the standard deviation, than it is fine to write

$1.23 \pm 0.52$

with out the $\sigma$, as long as you make it clear that you are reporting the standard deviation and not a confidence interval, since many readers will assume this notation refers to a confidence interval. I've never seen the notation

$1.23 \pm 0.52\sigma$

used for this before, but it's possible it could be normal in your field. Unlikely though.

In the medical professional journals what John has written is commonly used as a quick summary description of the variable. The point that the symbol for sigma is left out is important because it could then be interpreted as a statistical interval such as a confidence interval. The first display is standard and usually does not require further explanation especially in abstracts where space can be strictly limited.

If it is the sampling distribution of the mean that you want to describe then you should use the standard error. But make sure that you state that at least the first time you use it in the paper. Even when you are doing the summary and therefore use the standard deviation it never hurts to at least mention the convention you are using for the paper upfront at the first instance.