Hi

I have a distribution for which I would like to use median say M. The problem is that I do not know how to define some range based on M+3 [math]\sigma[/math]. Is there some kind of variance related to median ?

Since you have the distribution why would you not simply calculate the variance from it?

If it is a binomial distribution then:

[math]\mu=np[/math]

[math]\sigma=(np(1-p))^{2}[/math]

so [math]\sigma=(\mu(1-p))^{2}[/math]

and in a normal distribution the medians is equal to the mean so you should be able to relate the two. Hope this helped.

In general if your distribution is symmetrical, then the median and mean are the same. Remember that the 3 sigma rule relates to normal distributions. If you do not have a normal distribution then the 99.7% does not apply. The percent might be higher or lower - it all depends on your data.