(Sidenote: First of all, I would like to point out that this wasn’t a post first for me, all answers were already shown, even after refreshing the page.)
I would start by explaining that the electron, from our perspective is moving around us in a circular motion. Imagine you take the heavy ball, hang it on a rope and fling that rope above you like a lasso. To take the time averaged position of this ball (the s-electron), you spin the lasso for a very very long time, this is a circular pattern, and then you take one piece out of it, to average it. Therefore the time averaged position would be a point on the circular path.