Why is standard deviation relevant to Brownian motion?

[Kork]

Can someone please explain how the standard deviation is relevant when we are talking Brownian motion? And why is statistics important when we want to understand the movement of a brownian particle?

 

[mathman]

The motion of individual particles is random. Statistics is used to estimate average properties, while standard deviations give some idea of the size of fluctuations.

http://en.wikipedia.org/wiki/Brownian_motion