Median and variance

[aus_fas]

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 ?

[timo]

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

[DJBruce]

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.

[stereologist]

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.