[SciPy-User] from 50% probablity value to standard deviation

[Christoph Deil]

On Jul 19, 2011, at 11:38 AM, Johannes Radinger wrote:

> Hello SciPy-People,
> 
> I have got a normal distribution with μ=0 and I know that 50% of all
> observations
> are within a certain range (50% probability are between -x and +x).
> How can I get the standard deviation of that normal distribution?
> Usually 68,3 % are within one SD. How is it possible to calculate the
> SD from my 50% value? Is there any conversion factor I can use? Can
> that be simply and exactly calculated with Scipy?
> 

You can get the conversion factor like this:
>>> scipy.stats.halfnorm.ppf(0.5)
0.67448975019608171

Here is how you use it to compute the standard deviation:
>>> sd = x / scipy.stats.halfnorm.ppf(0.5)

Christoph