# “Standard Deviation” of non-negative data

I've been asked to analyse the distribution of a set of data, essentially a single column of random samples of a physical parameter which cannot be negative. The standard deviation that I usually calculate assumes that data are normally distributed, which in this case cannot be true.

Since I'm used to being asked to provide the standard deviation and mean of a dataset as a measure of the errors, I'd like to know whether there is an easily calculated parameter for a more appropriate distribution that would fulfil the same purpose?

I apologise if this question is ill-posed; I am not a statistician by training.

With many thanks,

Loruschorus

• Because the standard deviation, as universally defined, makes no assumptions about normality--it's merely a sample statistic-- how does the SD that you "usually calculate" differ from it? – whuber Dec 19 '11 at 14:46
• This kind of comment, that standard deviation is defined only for normal distributions, or makes sense only for normal distributions, or the formula for standard deviation assumes that the data set is normally distributed, shows up so frequently here that it makes me wonder whether there is a commonly used textbook for a STAT 101 type course (or a popular web site that people visit frequently) which makes such claims or, more likely, makes statements that lead readers to make such unwarranted inferences. – Dilip Sarwate Dec 19 '11 at 16:12
• @Dilip There are estimates of standard deviation, often called "pseudo SDs," that assume approximate normality. One is the IQR divided by 1.35. Another is half the difference between the 84th and 16th sample percentiles. A deeper question lurking here is whether an estimated SD is an appropriate way to measure variation for a strikingly non-normal distribution. (Another issue is the implicit, but incorrect, assumption that positive values cannot be adequately modeled by normal distributions.) – whuber Dec 19 '11 at 16:34
• if, by positive the OP means asymetric and by Gaussian he means symmetric with square integrable tails then the OP has a point... – user603 Mar 10 '14 at 22:37